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Question 1 1 of 368 selected Inference From Sample Statistics And Margin Of Error H
Texting behaviorTalks on cell phone dailyDoes not talk on cell phone dailyTotal
Light110146256
Medium139164303
Heavy16674240
Total415384799

In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. Based on the data from the study, an estimate of the percent of US teens who are heavy texters is 30% and the associated margin of error is 3%. Which of the following is a correct statement based on the given margin of error?

  1. Approximately 3% of the teens in the study who are classified as heavy texters are not really heavy texters.

  2. It is not possible that the percent of all US teens who are heavy texters is less than 27%.

  3. The percent of all US teens who are heavy texters is 33%.

  4. It is doubtful that the percent of all US teens who are heavy texters is 35%.

Show Answer Correct Answer: D

Choice D is correct. The given margin of error of 3% indicates that the actual percent of all US teens who are heavy texters is likely within 3% of the estimate of 30%, or between 27% and 33%. Therefore, it is unlikely, or doubtful, that the percent of all US teens who are heavy texters would be 35%.

Choice A is incorrect. The margin of error doesn’t provide any information about the accuracy of reporting in the study. Choice B is incorrect. Based on the estimate and given margin of error, it is unlikely that the percent of all US teens who are heavy texters would be less than 27%, but it is possible. Choice C is incorrect. While the percent of all US teens who are heavy texters is likely between 27% and 33%, any value within this interval is equally likely. We can’t be certain that the value is exactly 33%.

Question 2 2 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A printer produces posters at a constant rate of 42 posters per minute. At what rate, in posters per hour, does the printer produce the posters?

Show Answer Correct Answer: 2520

The correct answer is 2,520 . There are 60 minutes in one hour. At a rate of 42 posters per minute, the number of posters produced in one hour can be determined by (42 posters1  minute)(60 minutes1 hour), which is 2,520 posters per hour.

Question 3 3 of 368 selected Probability And Conditional Probability H
Number of Contestants by Score and Day
 5 out
  of 5
4 out
  of 5
3 out
  of 5
2 out
  of 5
1 out
  of 5
0 out
  of 5
Total
Day 123462320
Day 223554120
Day 333453220
Total7913169660

The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above.

No contestant received the same score on two different days. If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?

Show Answer

The correct answer is five sevenths. It is given that no contestant received the same score on two different days, so each of the contestants who received a score of 5 is represented in the “5 out of 5” column of the table exactly once. Therefore, the probability of selecting a contestant who received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days, is found by dividing the total number of contestants who received a score of 5 on Day 2 or Day 3 2 plus 3, equals 5 by the total number of contestants who received a score of 5, which is given in the table as 7. So the probability is five sevenths. Note that 5/7, .7142, .7143, and 0.714 are examples of ways to enter a correct answer.

Question 4 4 of 368 selected Probability And Conditional Probability E

Each face of a fair 14 -sided die is labeled with a number from 1 through 14 , with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2 ?

  1. 1 14

  2. 214

  3. 1214

  4. 13 14

Show Answer Correct Answer: A

Choice A is correct. The total number of possible outcomes for rolling a fair 14 -sided die is 14 . The number of possible outcomes for rolling a 2 is 1 . The probability of rolling a 2 is the number of possible outcomes for rolling a 2 divided by the total number of possible outcomes, or 114.

Choice B is incorrect. This is the probability of rolling a number no greater than 2 .

Choice C is incorrect. This is the probability of rolling a number greater than 2 .

Choice D is incorrect. This is the probability of rolling a number other than 2 .

Question 5 5 of 368 selected Inference From Sample Statistics And Margin Of Error E

There are 55 students in Spanish club. A sample of the Spanish club students was selected at random and asked whether they intend to enroll in a new study program. Of those surveyed, 20% responded that they intend to enroll in the study program. Based on this survey, which of the following is the best estimate of the total number of Spanish club students who intend to enroll in the study program?

  1. 11

  2. 20

  3. 44

  4. 55

Show Answer Correct Answer: A

Choice A is correct. It’s given that 20% of the students surveyed responded that they intend to enroll in the study program. Therefore, the proportion of students in Spanish club who intend to enroll in the study program, based on the survey, is 0.20. Since there are 55 total students in Spanish club, the best estimate for the total number of these students who intend to enroll in the study program is 55(0.20), or 11 .

Choice B is incorrect. This is the best estimate for the percentage, rather than the total number, of students in Spanish club who intend to enroll in the study program.

Choice C is incorrect. This is the best estimate for the total number of Spanish club students who do not intend to enroll in the study program.

Choice D is incorrect. This is the total number of students in Spanish club.

Question 6 6 of 368 selected Percentages H

Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is three fourths cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. If p percent of an adult’s daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x ?

  1. p equals, 0 point 5 x

  2. p equals, 5 x

  3. p equals, open parenthesis, 0 point 0 5, close parenthesis, to the x power

  4. p equals, open parenthesis, 1 point 0 5, close parenthesis, to the x power

Show Answer Correct Answer: B

Choice B is correct. It’s given that each serving of Crunchy Grain cereal provides 5% of an adult’s daily allowance of potassium, so x servings would provide x times 5%. The percentage of an adult’s daily allowance of potassium, p, is 5 times the number of servings, x. Therefore, the percentage of an adult’s daily allowance of potassium can be expressed as p equals 5 x.

Choices A, C, and D are incorrect and may result from incorrectly converting 5% to its decimal equivalent, which isn’t necessary since p is expressed as a percentage. Additionally, choices C and D are incorrect because the context should be represented by a linear relationship, not by an exponential relationship.

 

Question 7 7 of 368 selected Percentages H

The expression 0.35 x  represents the result of decreasing a positive quantity x by what percent?

  1. 3.5%

  2. 35%

  3. 6.5%

  4. 65%

Show Answer Correct Answer: D

Choice D is correct. Let n% represent the percent by which the positive quantity x is decreased to result in 0.35 x . The value of n can be found by solving the equation x-(n100)x=0.35x. Since x is a common factor of each of the terms on the left-hand side of this equation, the equation can be rewritten as x(1-n100)=0.35x. Dividing each side of this equation by x yields 1-n100=0.35. Multiplying each side of this equation by 100 yields 100-n=35. Subtracting 100 from each side of this equation yields - n = - 65 . Dividing each side of this equation by - 1 yields n = 65 . Therefore, the expression 0.35 x represents the result of decreasing the positive quantity x by 65%.

Choice A is incorrect. Decreasing the quantity x by 3.5% yields x-0.035x, or 0.965 x , not 0.35 x .

Choice B is incorrect. Decreasing the quantity x by 35% yields x-0.35x, or 0.65 x , not 0.35 x .

Choice C is incorrect. Decreasing the quantity x by 6.5% yields x-0.065x, or 0.935 x , not 0.35 x .

Question 8 8 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

4 , 10 , 18 , 4 , 4 , 5 , 6 , 5

What is the median of the data set shown?

  1. 4

  2. 5

  3. 7

  4. 14

Show Answer Correct Answer: B

Choice B is correct. If a data set contains an even number of data values, when the data values are listed in ascending or descending order, the median is between the two middle values. The given data set contains 8 values. When listed in ascending order, the data set is 4 , 4 , 4 , 5 , 5 , 6 , 10 , 18 and the two middle values are 5 and 5 . Since the two middle values are the same, the median must be 5 .

Choice A is incorrect. This value is between the two middle values in the list shown, not the two middle values when the data values are listed in ascending or descending order.

Choice C is incorrect. This is the mean, not the median, of the data set.

Choice D is incorrect. This is the range, not the median, of the data set.

Question 9 9 of 368 selected Probability And Conditional Probability M
Prices of 14 Different Cars
Type of carPriced at no more
 than $25,000
Priced greater
 than $25,000
Total
Nonhybrid538
Hybrid246
Total7714
The table above shows information about 14 cars listed for sale on an auto dealership’s website. If one of the cars listed for sale is selected at random, what is the probability that the car selected will be a hybrid car priced at no more than $25,000 ?
  1. one seventh

  2. two sevenths

  3. one third

  4. four sevenths

Show Answer Correct Answer: A

Choice A is correct. It’s given that there are 2 hybrid cars priced at no more than $25,000. It’s also given that there are 14 cars total for sale. Therefore, the probability of selecting a hybrid priced at no more than $25,000 when one car is chosen at random is 2 over 14 equals one seventh.

Choice B is incorrect. This is the probability of selecting a hybrid car priced greater than $25,000 when choosing one car at random. Choice C is incorrect. This is the probability, when choosing randomly from only the hybrid cars, of selecting one priced at no more than $25,000. Choice D is incorrect. This is the probability of selecting a hybrid car when selecting at random from only the cars priced greater than $25,000.

 

Question 10 10 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

The International Space Station orbits Earth at an average speed of 4.76 miles per second. What is the space station’s average speed in miles per hour?

  1. 285.6

  2. 571.2

  3. 856.8

  4. 17,136.0

Show Answer Correct Answer: D

Choice D is correct. Since 1 minute = 60 seconds and 1 hour = 60 minutes, it follows that 1 hour = (60)(60), or 3,600 seconds. Using this conversion factor, the space station’s average speed of 4.76 miles per second is equal to an average speed of the fraction with numerator 4 point 7 6 miles, and denominator second, times, the fraction with numerator 3,600 seconds, and denominator hour, equals, the fraction with numerator 17,136 miles, and denominator hour, or 17,136 miles per hour.

Choice A is incorrect. This is the space station’s average speed in miles per minute. Choice B is incorrect. This is double the space station’s average speed in miles per minute, or the number of miles the space station travels on average in 2 minutes. Choice C is incorrect. This is triple the space station’s average speed in miles per minute, or the number of miles the space station travels on average in 3 minutes. 

Question 11 11 of 368 selected Two-Variable Data: Models And Scatterplots M

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. Which of the following is closest to the difference between the y-coordinate of the data point with x equals 1 and the y-value predicted by the line of best fit at x equals 1 ?

The figure presents a scatterplot in the x y plane. The numbers 0 through 6, in increments of 1, are indicated on the x-axis. The numbers 6 through 12, in increments of 1, are indicated on the y-axis. There are 10 data points in the scatterplot. The data points begin at the point with coordinates 0 comma 12, and trend downward and to the right. The coordinates of the data points are as follows. Note that all values are approximate.
Point 1. 0, comma 12.
Point 2. 0 point 8, comma 11.
Point 3. 1, comma 12.
Point 4. 1 point 5, comma 10 point 3.
Point 5. 2, comma 10.
Point 6. 2 point 2, comma 9 point 2.
Point 7. 3, comma 9.
Point 8. 3 point 5, comma 8.
Point 9. 3 point 8, comma 8 point 3.
Point 10. 4, comma 7.

A line of best fit is also drawn. The line slants downward and to the right, passing through the point with approximate coordinates 1 comma 11, and the point with approximate coordinates 4 comma 7 point 5.

  1. 1

  2. 2

  3. 5

  4. 12

Show Answer Correct Answer: A

Choice A is correct. The data point with x equals 1 has a y-coordinate of 12. The y-value predicted by the line of best fit at x equals 1 is approximately 11. The difference between the y-coordinate of the data point and the y-value predicted by the line of best fit at x equals 1 is 12 minus 11, or 1.

Choices B and C are incorrect and may result from incorrectly reading the scatterplot. Choice D is incorrect. This is the y-coordinate of the data point at x equals 1.

Question 12 12 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

For a person m miles from a flash of lightning, the length of the time interval from the moment the person sees the lightning to the moment the person hears the thunder is k seconds. The ratio of m to k can be estimated to be 1 to 5. According to this estimate, the person is how many miles from a flash of lightning if the time interval is 25 seconds?

  1. 10

  2. 9

  3. 6

  4. 5

Show Answer Correct Answer: D

Choice D is correct. It’s given that the ratio of m to k is estimated to be 1 to 5. Therefore, when k equals 25, the relationship between these ratios can be expressed by the proportion m over 25, equals one fifth. Multiplying both sides of this equation by 25 yields m equals 5.

Choices A, B, and C are incorrect and may result from calculation errors.

Question 13 13 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

The population density of Iceland, in people per square kilometer of land area, increased from 2.5 in 1990 to 3.3 in 2014. During this time period, the land area of Iceland was 100,250 square kilometers. By how many people did Iceland’s population increase from 1990 to 2014?

  1. 330,825

  2. 132,330

  3. 125,312

  4. 80,200

Show Answer Correct Answer: D

Choice D is correct. The increase in Iceland’s population can be found by multiplying the increase in population density, in people per square kilometer, by the area, in square kilometers. It’s given that the population density of Iceland was 2.5 people per square kilometer in 1990 and 3.3 people per square kilometer in 2014. The increase in population density can be found by subtracting 2.5 from 3.3, which yields 0.8. It’s given that the land area of Iceland was 100,250 square kilometers. Thus, the increase in population is 0 point 8 times 100,250, or 80,200.

Alternate approach: It’s given that the population density of Iceland, in people per square kilometer of land area, in 1990 was 2.5. Since the land area of Iceland was 100,250 square kilometers, it follows that the population of Iceland in 1990 was 2 point 5 times 100,250, or 250,625. Similarly, the population of Iceland in 2014 was 3 point 3 times 100,250, or 330,825. The population increase is the difference in the population from 1990 to 2014, or 330,825 minus 250,625, which yields 80,200. Therefore, Iceland’s population increased by 80,200 from 1990 to 2014.

Choice A is incorrect. This is the population of Iceland in 2014. Choice B is incorrect and may result from dividing 3.3 by 2.5, instead of subtracting 2.5 from 3.3. Choice C is incorrect and may result from dividing the population of Iceland in 1990 by 2.

Question 14 14 of 368 selected Inference From Sample Statistics And Margin Of Error H
Views on Nuclear Energy Use
ResponseFrequency
Strongly favor56
Somewhat favor214
Somewhat oppose104
Strongly oppose37

A researcher interviewed 411 randomly selected US residents and asked about their views on the use of nuclear energy. The table above summarizes the responses of the interviewees. If the population of the United States was 300 million when the survey was given, based on the sample data for the 411 US residents, what is the best estimate, in millions, of the difference between the number of US residents who somewhat favor or strongly favor the use of nuclear energy and the number of those who somewhat oppose or strongly oppose it? (Round your answer to the nearest whole number.)

Show Answer

The correct answer is 94. Of those interviewed, 56 plus 214, equals 270 “strongly favor” or “somewhat favor” the use of nuclear energy, and 104 plus 37, equals 141 interviewees “somewhat oppose” or “strongly oppose” the use of nuclear energy. The difference between the sizes of the two surveyed groups is 270 minus 141, equals 129. The proportion of this difference among the entire group of interviewees is the fraction 129 over 411. Because the sample of interviewees was selected at random from US residents, it is reasonable to assume that the proportion of this difference is the same among all US residents as in the sample. Therefore, the best estimate, in millions, of the difference between the number of US residents who somewhat favor or strongly favor the use of nuclear energy and the number of those who somewhat oppose or strongly oppose it is the fraction 129 over 411, end fraction, times 300, which to the nearest million is 94.

Question 15 15 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

The seven data values 2, 2, 2, 3, 4, 4, 11 are shown.

What is the median of the seven data values shown?

  1. 2

  2. 3

  3. 4

  4. 9

Show Answer Correct Answer: B

Choice B is correct. When a data set has an odd number of values, the median can be found by ordering the values from least to greatest and determining the value in the middle. Since the values are already presented in order from least to greatest and there are 7 values, the median is the fourth value in the list. Therefore, the median is 3.

Choice A is incorrect. This is the mode. Choice C is incorrect. This is the mean. Choice D is incorrect. This is the range.

 

Question 16 16 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

  • From left to right the values of the vertical bars in the Group 1 box plot are as follows:
    • First vertical bar: 21
    • Second vertical bar: 22
    • Third vertical bar: 25
    • Fourth vertical bar: 26
    • Fifth vertical bar: 28
  • From left to right the values of the vertical bars in the Group 2 box plot are as follows:
    • First vertical bar: 22
    • Second vertical bar: 23
    • Third vertical bar: 24
    • Fourth vertical bar: 25
    • Fifth vertical bar: 28

The box plots summarize the masses, in kilograms, of two groups of gazelles. Based on the box plots, which of the following statements must be true?

  1. The mean mass of group 1 is greater than the mean mass of group 2.

  2. The mean mass of group 1 is less than the mean mass of group 2.

  3. The median mass of group 1 is greater than the median mass of group 2.

  4. The median mass of group 1 is less than the median mass of group 2.

Show Answer Correct Answer: C

Choice C is correct. The median of a data set represented in a box plot is represented by the vertical line within the box. It follows that the median mass of the gazelles in group 1 is 25 kilograms, and the median mass of the gazelles in group 2 is 24 kilograms. Since 25 kilograms is greater than 24 kilograms, the median mass of group 1 is greater than the median mass of group 2 .

Choice A is incorrect. The mean mass of each of the two groups cannot be determined from the box plots.

Choice B is incorrect. The mean mass of each of the two groups cannot be determined from the box plots.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 17 17 of 368 selected Percentages H

A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?

Show Answer

The correct answer is 8. The 6 students represent open parenthesis, 100 minus 15, minus 45, minus 25, close parenthesis, percent, equals 15 percent of those invited to join the committee. If x people were invited to join the committee, then 0 point 1 5 x, equals 6. Thus, there were 6 over, 0 point 1 5, equals 40 people invited to join the committee. It follows that there were 0 point 4 5 times 40, equals 18 teachers and 0 point 2 5 times 40, equals 10 school and district administrators invited to join the committee. Therefore, there were 8 more teachers than school and district administrators invited to join the committee.

Question 18 18 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

The ratio 140 to m is equivalent to the ratio 4 to 28 . What is the value of m ?

Show Answer Correct Answer: 980

The correct answer is 980 . It's given that the ratio 140 to m is equivalent to the ratio 4 to 28 . Therefore, the value of m can be found by solving the equation 140m=428. Multiplying each side of this equation by m yields 140=4m28. Multiplying each side of this equation by 28 yields 3,920 = 4 m . Dividing each side of this equation by 4 yields 980 = m . Therefore, the value of m is 980 .

Question 19 19 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A customer spent $27 to purchase oranges at $3 per pound. How many pounds of oranges did the customer purchase?

Show Answer Correct Answer: 9

The correct answer is 9 . It’s given that the customer spent $27 to purchase oranges at $3 per pound. Therefore, the number of pounds of oranges the customer purchased is $27(1 pound$3), or 9 pounds.

Question 20 20 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A mechanical device in a workshop produces items at a constant rate of 60 items per hour. At this rate, how many items will the mechanical device produce in 3 hours?

Show Answer Correct Answer: 180

The correct answer is 180 . It’s given that a mechanical device produces items at a constant rate of 60 items per hour. This rate can be written as 60 items1 hour. Let x represent the number of items the mechanical device will produce in 3 hours at the given rate. It follows that 60 items1 hour=x items3 hours, which can be written as 601=x3, or 60=x3. Multiplying each side of this equation by 3 yields 180 = x . Therefore, at the given rate, the mechanical device will produce 180 items in 3 hours.

Alternate approach: It's given that a mechanical device produces items at a constant rate of 60 items per hour. At this rate, the mechanical device will produce (60 items1 hour)(3 hours), or 180 items in 3 hours.

Question 21 21 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments H

A sample of 40 fourth-grade students was selected at random from a certain school. The 40 students completed a survey about the morning announcements, and 32 thought the announcements were helpful. Which of the following is the largest population to which the results of the survey can be applied?

  1. The 40 students who were surveyed

  2. All fourth-grade students at the school

  3. All students at the school

  4. All fourth-grade students in the county in which the school is located

Show Answer Correct Answer: B

Choice B is correct. Selecting a sample of a reasonable size at random to use for a survey allows the results from that survey to be applied to the population from which the sample was selected, but not beyond this population. In this case, the population from which the sample was selected is all fourth-grade students at a certain school. Therefore, the results of the survey can be applied to all fourth-grade students at the school.

Choice A is incorrect. The results of the survey can be applied to the 40 students who were surveyed. However, this isn’t the largest group to which the results of the survey can be applied. Choices C and D are incorrect. Since the sample was selected at random from among the fourth-grade students at a certain school, the results of the survey can’t be applied to other students at the school or to other fourth-grade students who weren’t represented in the survey results. Students in other grades in the school or other fourth-grade students in the country may feel differently about announcements than the fourth-grade students at the school.

Question 22 22 of 368 selected Two-Variable Data: Models And Scatterplots E
The figure presents a scatterplot in the x y plane. The numbers 0 through 6, in increments of 1, are indicated on the x axis. The numbers 0 through 20, in increments of 2, are indicated on the y axis. There are 12 data points in the scatterplot. The data points are in the shape of a parabola that opens upward. The data points begin on the y axis at 20, and trend downward and to the right until they reach a first low point with coordinates 2 point 5 comma 5 and a second low point with coordinates 3 comma 5.  Then the data points trend upward and to the right until they reach the last point with coordinates 5 point 5 comma 20.

Of the following, which is the best model for the data in the scatterplot?

  1. y equals, 2 x squared, minus 11 x, minus 20

  2. y equals, 2 x squared, minus 11 x, plus 20

  3. y equals, 2 x squared, minus 5 x, minus 3

  4. y equals, 2 x squared, minus 5 x, plus 3

Show Answer Correct Answer: B

Choice B is correct. The graphical model that most closely fits the data in the scatterplot is a model in which the number of data points above and below the model are approximately balanced. Fitting a graphical model to the data shown results in an upward-facing parabola with a y-intercept near the point with coordinates 0 comma 20 and a vertex with an approximate x-value of 2.5. Of the given choices, only choice B gives an equation of an upward-facing parabola with a y-intercept at the point with coordinates 0 comma 20 . Furthermore, substituting 2.5 for x into the equation in choice B yields y equals 5. This is approximately the y-value of the vertex of the model.

Choices A, C, and D are incorrect. These equations don’t give a graphical model that best fits the data. At x equals 0, they have y-values of negative 20, negative 3, and 3, respectively. At x equals 2 point 5, they have y-values of negative 35, negative 3, and 3, respectively.

 

Question 23 23 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments M

Residents of a town were surveyed to determine whether they are satisfied with the concession stand at the local park. A random sample of 200 residents was selected. All 200 responded, and 87% said they are satisfied. Based on this information, which of the following statements must be true?

I. Of all the town residents, 87% would say they are satisfied with the concession stand at the local park.
II. If another random sample of 200 residents were surveyed, 87% would say they are satisfied.

  1. Neither

  2. I only

  3. II only

  4. I and II

Show Answer Correct Answer: A

Choice A is correct. The purpose of surveying a random sample of residents is to approximate the percent of the town residents that are satisfied with the concession stand. The sample doesn’t necessarily get the same result as surveying every resident of the town, nor would another sample necessarily have identical results. Therefore, although it’s possible that either statement I or statement II could prove true by surveying every resident of the town, these statements cannot be proven true solely based on the results of the sample.

Choice B is incorrect because surveying a sample of the town residents may not have the same result as surveying all the town residents. Choices C and D are incorrect because surveying a different sample of residents could yield different results.

Question 24 24 of 368 selected Two-Variable Data: Models And Scatterplots E

The figure presents a scatterplot titled “Temperature of a Cup of Coffee during an Experiment.” The horizontal axis is labeled “Time since cup was removed from heat source, in minutes,” and the numbers 0 through 140, in increments of 20, are indicated. The vertical axis is labeled “Temperature, in degrees Fahrenheit,” and the numbers 0 through 220, in increments of 20, are indicated. There are 15 data points in the scatterplot. The data points begin with point 0 comma 195, and trend downward and to the right, rapidly at first, then more and more slowly, finally leveling off. The last data point is 140 comma 76. The 15 data points are as follows. The second coordinate of each point is approximate. Point 1, 0 comma 195. Point 2, 10 comma 153. Point 3, 20 comma 136. Point 4, 30 comma 122. Point 5, 40 comma 109. Point 6, 50 comma 100. Point 7, 60 comma 92. Point 8, 70 comma 84. Point 9, 80 comma 82. Point 10, 90 comma 80. Point 11, 100 comma 79. Point 12, 110 comma 77. Point 13, 120 comma 77. Point 14, 130 comma 76. Point 15, 140 comma 76.

In an experiment, a heated cup of coffee is removed from a heat source, and the cup of coffee is then left in a room that is kept at a constant temperature. The graph above shows the temperature, in degrees Fahrenheit (°F), of the coffee immediately after being removed from the heat source and at 10-minute intervals thereafter. During which of the following 10-minute intervals does the temperature of the coffee decrease at the greatest average rate?

  1. Between 0 and 10 minutes

  2. Between 30 and 40 minutes

  3. Between 50 and 60 minutes

  4. Between 90 and 100 minutes

Show Answer Correct Answer: A

Choice A is correct. The average rate of change in temperature of the coffee in degrees Fahrenheit per minute is calculated by dividing the difference between two recorded temperatures by the number of minutes in the corresponding interval of time. Since the time intervals given are all 10 minutes, the average rate of change is greatest for the points with the greatest difference in temperature. Of the choices, the greatest difference in temperature occurs between 0 and 10 minutes.

Choices B, C, and D are incorrect and may result from misinterpreting the average rate of change from the graph.

Question 25 25 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

How many fluid ounces are equivalent to 76 quarts? (8 fluid ounces=1 cup and 4 cups=1 quart)

Show Answer Correct Answer: 2432

The correct answer is 2,432 . It's given that 4 cups=1 quart. It follows that 76 quarts is equivalent to (76 quarts)(4 cups1 quart), or 304 cups. It's also given that 8 fluid ounces=1 cup. It follows that 304 cups is equivalent to (304 cups)(8 fluid ounces1 cup), or 2,432 fluid ounces.

Question 26 26 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

Ages of 20 Students Enrolled in a College Class 

Age Frequency
18 6
19 5
20 4
21 2
22 1
23 1
30 1

The table above shows the distribution of ages of the 20 students enrolled in a college class. Which of the following gives the correct order of the mean, median, and mode of the ages?

  1. mode < median < mean

  2. mode < mean < median

  3. median < mode < mean

  4. mean < mode < median

Show Answer Correct Answer: A

Choice A is correct. The mode is the data value with the highest frequency. So for the data shown, the mode is 18. The median is the middle data value when the data values are sorted from least to greatest. Since there are 20 ages ordered, the median is the average of the two middle values, the 10th and 11th, which for these data are both 19. Therefore, the median is 19. The mean is the sum of the data values divided by the number of the data values. So for these data, the mean is the fraction with numerator, open parenthesis, 18 times 6, close parenthesis, plus, open parenthesis, 19 times 5, close parenthesis, plus, open parenthesis, 20 times 4, close parenthesis, plus, open parenthesis, 21 times 2, close parenthesis, plus, open parenthesis, 22 times 1, close parenthesis, plus, open parenthesis, 23 times 1, close parenthesis, plus, open parenthesis, 30 times 1, close parenthesis, and denominator 20, equals 20.

Since the mode is 18, the median is 19, and the mean is 20, mode is less than median, which is less than mean.

Choices B and D are incorrect because the mean is greater than the median. Choice C is incorrect because the median is greater than the mode.

Alternate approach: After determining the mode, 18, and the median, 19, it remains to determine whether the mean is less than 19 or more than 19. Because the mean is a balancing point, there is as much deviation below the mean as above the mean. It is possible to compare the data to 19 to determine the balance of deviation above and below the mean. There is a total deviation of only 6 below 19 (the 6 values of 18); however, the data value 30 alone deviates by 11 above 19. Thus the mean must be greater than 19.

Question 27 27 of 368 selected Probability And Conditional Probability E
Colors of Marbles in a Bag
ColorNumber
Red8
Blue10
Green22
Total40

The table shows the number of different colors of marbles in a bag. If a marble is chosen at random from the bag, what is the probability that the marble will be blue?

  1. 30 over 40

  2. 22 over 40

  3. 18 over 40

  4. 10 over 40

Show Answer Correct Answer: D

Choice D is correct. If a marble is chosen at random from the bag, the probability of choosing a marble of a certain color is the number of marbles of that color divided by the total number of marbles in the bag. Since there are 10 blue marbles in the bag, and there are 40 total marbles in the bag, the probability that the marble chosen will be blue is 10 over 40.

Choices A, B, and C are incorrect. These represent the probability that the marble chosen won’t be blue (choice A), will be green (choice B), and won’t be green (choice C).

 

Question 28 28 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

The bar graph summarizes the charge, in kilowatt-hours (kWh), a battery received each day for 15 days.

76543210Number of days089111623Charge (kWh)
  • The data for the 6 categories are as follows:
    • 0 kilowatt-hours: 6
    • 8 kilowatt-hours: 1
    • 9 kilowatt-hours: 2
    • 11 kilowatt-hours: 4
    • 16 kilowatt-hours: 1
    • 23 kilowatt-hours: 1

For how many of these 15 days did the battery receive a charge of 0 kWh?

  1. 0

  2. 1

  3. 4

  4. 6

Show Answer Correct Answer: D

Choice D is correct. It's given that the bar graph summarizes the charge, in kilowatt-hours (kWh), a battery received each day for 15 days. The height of each bar in the bar graph shown represents the number of days the battery received the charge, in kWh, specified at the bottom of the bar. The bar for a charge of 0 kWh reaches a height of 6 . Therefore, the battery received a charge of 0 kWh for 6 of these days.

Choice A is incorrect. This is the charge, in kWh, that the battery received, not the number of days the battery received this charge.

Choice B is incorrect. This is the number of days the battery received a charge of either 8 , 16 , or 23 kWh.

Choice C is incorrect. This is the number of days the battery received a charge of 11 kWh.

Question 29 29 of 368 selected Probability And Conditional Probability E
 
Customer Purchases at a Gas Station
 Beverage purchasedBeverage not purchasedTotal
Gasoline purchased602585
Gasoline not purchased351550
Total9040135

On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?

  1. 15 over 50

  2. 15 over 40

  3. 35 over 50

  4. 50 over 135

Show Answer Correct Answer: D

Choice D is correct. The total number of gas station customers on Tuesday was 135. The table shows that the number of customers who did not purchase gasoline was 50. Finding the ratio of the number of customers who did not purchase gasoline to the total number of customers gives the probability that a customer selected at random on that day did not purchase gasoline, which is 50 over 135.

Choice A is incorrect and may result from finding the probability that a customer did not purchase a beverage, given that the customer did not purchase gasoline. Choice B is incorrect and may result from finding the probability that a customer did not purchase gasoline, given that the customer did not purchase a beverage. Choice C is incorrect and may result from finding the probability that a customer did purchase a beverage, given that the customer did not purchase gasoline.

 

Question 30 30 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

4 , 4 , 4 , 4 , 8 , 8 , 8 , 13 , 13

Which frequency table correctly represents the data listed?

Show Answer Correct Answer: A

Choice A is correct. A frequency table is a table that lists the data value and shows the number of times the data value occurs. In the data listed, the number 4 occurs four times, the number 8 occurs three times, and the number 13 occurs two times. This corresponds to the table in choice A.

Choice B is incorrect. This table has the values for number and frequency reversed.

Choice C is incorrect because the frequency values don't represent the data listed.

Choice D is incorrect. This table represents the listed number values as the frequency values.

Question 31 31 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A group of monarch butterflies migrated from Chicago, Illinois, to Michoacán, Mexico, flying a total of 2,100 miles. It took a single butterfly in the group 120 days to travel this route one way. On average, how many miles did the butterfly travel per day?

  1. 0.057

  2. 0.729

  3. 17.5

  4. 24

Show Answer Correct Answer: C

Choice C is correct. If the butterfly traveled 2,100 miles in 120 days, then it traveled, on average, 2,100 miles over 120 days equals, 17 point 5 miles per day.

Choice A is incorrect. This is approximately the average amount of time, in days, it took the butterfly to fly one mile: 120 days over 2,100 miles equals, 0 point 0 5 7 days per mile. Choice B is incorrect and may result from an arithmetic error. Choice D is incorrect. This is the number of hours in a day rather than the number of miles flown per day.

Question 32 32 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M
Data value Frequency
6 3
7 3
8 8
9 8
10 9
11 11
12 9
13 0
14 6

The frequency table summarizes the 57 data values in a data set. What is the maximum data value in the data set?

Show Answer Correct Answer: 14

The correct answer is 14 . The maximum value is the largest value in the data set. The frequency refers to the number of times a data value occurs. The given frequency table shows that for this data set, the data value 6 occurs three times, the data value 7 occurs three times, the data value 8 occurs eight times, the data value 9 occurs eight times, the data value 10 occurs nine times, the data value 11 occurs eleven times, the data value 12 occurs nine times, the data value 13 occurs zero times, and the data value 14 occurs six times. Therefore, the maximum data value in the data set is 14 .

Question 33 33 of 368 selected Probability And Conditional Probability M
Coat color Eye color
Deep blue Light brown Total
Cream-tortoiseshell 16 16 32
Chocolate 12   4 16
Total 28 20 48

The data on the coat color and eye color for 48 Himalayan kittens available for adoption were collected and summarized in the table above. What fraction of the chocolate-colored kittens has deep blue eyes?

  1. the fraction 12 over 48
  2. the fraction 12 over 28
  3. the fraction 16 over 32
  4. the fraction 12 over 16
Show Answer Correct Answer: D

Choice D is correct. The table shows that there are a total of 16 kittens that have a chocolate-colored coat. Of the 16 with a chocolate-colored coat, 12 have deep blue eyes. Therefore, the fraction of chocolate-colored kittens with deep blue eyes is simply the ratio of those two numbers, or the fraction 12 over 16.

Choice A is incorrect; this is the fraction of all chocolate-colored kittens. Choice B is incorrect; this is the fraction of kittens with deep blue eyes that have a chocolate-colored coat. Choice C is incorrect; this is the fraction of cream-tortoiseshell-colored kittens with deep blue eyes.

Question 34 34 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

If x y = 4 and 24 x n y = 4 , what is the value of n ?

Show Answer Correct Answer: 24

The correct answer is 24 . The equation 24xny=4 can be rewritten as (24n)(xy)=4. It's given that x y = 4 . Substituting 4 for x y in the equation (24n)(xy)=4 yields (24n)(4)=4. Multiplying both sides of this equation by n yields (24)(4)=4n. Dividing both sides of this equation by 4 yields 24 = n . Therefore, the value of n is 24 .

Question 35 35 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the relationship between two variables, x and y . A line of best fit is also shown.

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending down from left to right.
  • A line of best fit is shown:
    • The line of best slants down from left to right.
    • 1 point is touching the line of best fit.
    • 4 points are above the line of best fit.
    • 5 points are below the line of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (2 comma 12)
      • (8 comma 7)
      • (13 comma 3)

Which of the following equations best represents the line of best fit shown?

  1. y=13.5+0.8x

  2. y=13.5-0.8x

  3. y=-13.5+0.8x

  4. y=-13.5-0.8x

Show Answer Correct Answer: B

Choice B is correct. The line of best fit shown intersects the y-axis at a positive y-value and has a negative slope. The graph of an equation of the form y=a+bx, where a and b are constants, intersects the y-axis at a y-value of a and has a slope of b . Of the given choices, only choice B represents a line that intersects the y-axis at a positive y-value, 13.5 , and has a negative slope, -0.8 .

Choice A is incorrect. This equation represents a line that has a positive slope, not a negative slope.

Choice C is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value, and has a positive slope, not a negative slope.

Choice D is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value.

Question 36 36 of 368 selected Percentages M

In a sample, 80% of the items are faulty. There are 88 faulty items in the sample. How many total items are in the sample?

Show Answer Correct Answer: 110

The correct answer is 110 . Let x represent the total number of items in the sample. It’s given that 80% of the items are faulty and that there are 88 faulty items in the sample. Therefore, 80% of x is 88 . Since 80% can be rewritten as 80100, it follows that 80100x=88. Multiplying both sides of this equation by 100 yields 80 x = 8,800 . Dividing both sides of this equation by 80 yields x = 110 . Therefore, there are 110 total items in the sample.

Question 37 37 of 368 selected Two-Variable Data: Models And Scatterplots E

The figure presents a scatterplot titled “Temperature and Elevation.” The horizontal axis is labeled “Elevation, in feet,” and the numbers 6,000 through 9,000, in increments of 500, are indicated. The vertical axis is labeled “Temperature, in degrees Fahrenheit,” and the integers 37 through 45 are indicated. There are 8 data points. The data points begin a little below, and to the right of the top of the vertical axis, then trend downward and to the right. A line of best fit is drawn. The data represented by the 8 data points are as follows. Note that all values are approximate. Point 1. 6,350 feet, 42 point 9 degrees Fahrenheit. Point 2. 6,750 feet, 43 point 8 degrees Fahrenheit. Point 3. 6,750 feet, 42 degrees Fahrenheit. Point 4. 7,500 feet, 42 point 2 degrees Fahrenheit. Point 5. 8,000 feet, 40 point 5 degrees Fahrenheit. Point 6. 8,000 feet, 40 degrees Fahrenheit. Point 7. 8,800 feet, 38 point 6 degrees Fahrenheit. Point 8. 8,800 feet, 37 point 6 degrees Fahrenheit. The line of best fit passes through the data point representing 7,500 feet comma 41 point 1 degrees Fahrenheit, and the data point representing 8,500 feet comma 39 degrees Fahrenheit

The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. What temperature is predicted by the line of best fit for a location in the Lake Tahoe Basin with an elevation of 8,500 feet?

  1. 37°F

  2. 39°F

  3. 41°F

  4. 43°F

Show Answer Correct Answer: B

Choice B is correct. The line of best fit passes through the point with coordinates 8,500 comma 39. Therefore, the line of best fit predicts a temperature of 39°F for a location in Lake Tahoe Basin with an elevation of 8,500 feet.

Choice A is incorrect. This is the lowest temperature listed on the scatterplot, and the line of best fit never crosses this value for any of the elevations shown. Choice C is incorrect. According to the line of best fit, the temperature of 41°F is predicted for an elevation of slightly greater than 7,500 feet, not an elevation of 8,500 feet. Choice D is incorrect. According to the line of best fit, the temperature of 43°F is predicted for an elevation of roughly 6,700 feet, not an elevation of 8,500 feet.

Question 38 38 of 368 selected Probability And Conditional Probability E
Number of High School Students Who
Completed Summer Internships
High schoolYear
20082009201020112012
Foothill8780757670
Valley4454657682
Total131134140152152

The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Of the students who completed a summer internship in 2010, which of the following represents the fraction of students who were from Valley High School?

  1. 10 over 140

  2. 65 over 140

  3. 75 over 140

  4. 65 over 75

Show Answer Correct Answer: B

Choice B is correct. According to the table, 140 students from the two high schools completed summer internships in 2010. Of these, 65 were from Valley High School. Therefore, of the students who completed summer internships in 2010, the fraction 65 over 140 represents the fraction who were from Valley High School.

Choice A is incorrect. This is the difference between the numbers of students from the two high schools who completed internships in 2010 divided by the total number of students from the two schools who completed internships that year. Choice C is incorrect. This is the fraction of students from Foothill High School who completed internships out of all the students who completed internships in 2010. Choice D is incorrect. This is the number of students from Valley High School who completed internships in 2010 divided by the number of students from Foothill High School who completed internships in 2010.

Question 39 39 of 368 selected Percentages E

Of 300,000 paper clips, 234,000 are size large. What percentage of the paper clips are size large?

  1. 22 %

  2. 33 %

  3. 66 %

  4. 78 %

Show Answer Correct Answer: D

Choice D is correct. The proportion of the paper clips that are size large can be written as 234,000300,000, or 0.78 . Therefore, the percentage of the paper clips that are size large is 0.78(100), or 78%.

Choice A is incorrect. This is the percentage of the paper clips that are not size large.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 40 40 of 368 selected Percentages H

The positive number a is 2,241% of the sum of the positive numbers b and c , and b is 83% of c . What percent of b is a ?

  1. 23.24%

  2. 49.41%

  3. 2,324%

  4. 4,941%

Show Answer Correct Answer: D

Choice D is correct. It’s given that a is 2,241% of the sum of b and c . This can be represented by the equation a=(2,241100)(b+c), or a=22.41(b+c). It’s also given that that b is 83% of c . This can be represented by the equation b=(83100)c, or b=0.83c. Dividing both sides of this equation by 0.83 yields b0.83=c. Substituting b0.83 for c in the equation a=22.41(b+c) yields a=22.41(b+b0.83), or a=22.41(1.83b0.83), which is equivalent to a=41.0103b0.83, or a=49.41b. This equation is equivalent to a=(4,941100)b; therefore, a is 4,941% of b .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 41 41 of 368 selected Probability And Conditional Probability E
Voice type Number of singers
Countertenor 4
Tenor 6
Baritone 10
Bass 5

A total of 25 men registered for singing lessons. The frequency table shows how many of these singers have certain voice types. If one of these singers is selected at random, what is the probability he is a baritone?

  1. 0.10

  2. 0.40

  3. 0.60

  4. 0.67

Show Answer Correct Answer: B

Choice B is correct. This probability is calculated by dividing the number of baritone singers by the total number of men registered for singing lessons. It’s given that a total of 25 men registered for singing lessons and that there are 10 baritones. Therefore, the probability of selecting a baritone from this group at random is 10 over 25, which is equivalent to 0.40.

Choice A is incorrect. This would be the probability of selecting a baritone at random if there were 100 total men who registered for singing lessons. Choice C is incorrect. This is the probability of selecting a singer at random who isn’t a baritone. Choice D is incorrect. This would be the probability of selecting a baritone at random if there were 15 total men registered for singing lessons.

Question 42 42 of 368 selected Two-Variable Data: Models And Scatterplots H

  • The scatterplot has 6 data points.
  • The data points are in an exponential pattern trending down from left to right.
  • A curve of best fit is shown:
    • The curve of best fit trends down from left to right. 
    • The curve of best fit passes through the following approximate coordinates:
      • (0 comma 126)
      • (1 comma 105)
      • (5 comma 50)
      • (10 comma 20)

The scatterplot shows the relationship between two variables, x and y . An equation for the exponential model shown can be written as y=a(b)x, where a and b are positive constants. Which of the following is closest to the value of b ?

  1. 0.83

  2. 1.83

  3. 18.36

  4. 126.35

Show Answer Correct Answer: A

Choice A is correct. It's given that an equation for the exponential model shown can be written as y=a(b)x, where a and b are positive constants. For an exponential model written in this form, if the value of b is greater than 0 but less than 1 , the model is decreasing. If the value of b is greater than 1 , the model is increasing. The exponential model shown is decreasing. Therefore, the value of b is greater than 0 but less than 1 . Of the given choices, only 0.83 is a value greater than 0 but less than 1 . Thus, 0.83 is closest to the value of b .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 43 43 of 368 selected Percentages E

A table of the US minimum wage for 6 different years is shown below.

YearUS minimum wage
  (dollars per hour)
19601.00
19701.60
19803.10
19903.80
20005.15
20107.25
 

What was the percent increase of the minimum wage from 1960 to 1970?

  1. 30%

  2. 60%

  3. 62.5%

  4. 120%

Show Answer Correct Answer: B

Choice B is correct. According to the table, the minimum wage in 1960 was $1.00 per hour, and in 1970 it was $1.60 per hour. The percentage change is therefore 100 times open parenthesis, the fraction with numerator 1 point 6 0 minus 1 point 0 0, and denominator 1 point 0 0, close parenthesis, equals 60 percent.

Choice A is incorrect and may result from averaging the two wages before calculating the percentage change. Choice C is incorrect. This is the 1960 wage expressed as a percentage of the 1970 wage, not the percentage change between the two. Choice D is incorrect and may result from a calculation error.

Question 44 44 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

The bar graph shows the distribution of the number of students in each of four extracurricular activities at a high school.

6050403020100Number of studentschessdramaroboticsyearbook Activity
  • The Number of students data for the 4 bars are as follows:
    • chess: 30
    • drama: 40
    • robotics: 58
    • yearbook: 43

How many more students are in drama than in chess?

  1. 10

  2. 30

  3. 40

  4. 70

Show Answer Correct Answer: A

Choice A is correct. It's given that the bar graph shows the distribution of the number of students in each of four extracurricular activities at a high school. The bar representing drama has a height of 40 ; therefore, there are 40 students in drama. The bar representing chess has a height of 30 ; therefore, there are 30 students in chess. Thus, there are 40-30, or 10 more students in drama than in chess.

Choice B is incorrect. This is the number of students in chess.

Choice C is incorrect. This is the number of students in drama.

Choice D is incorrect. This is the sum of the number of students in drama and in chess.

Question 45 45 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

In a box of pens, the ratio of black pens to red pens is 8 to 1 . There are 40 black pens in the box. How many red pens are in the box?

  1. 5

  2. 8

  3. 40

  4. 320

Show Answer Correct Answer: A

Choice A is correct. It’s given that the ratio of black pens to red pens is 8 to 1 . Therefore, there are 18 as many red pens as black pens in the box. It’s also given that there are 40 black pens in the box. Therefore, the number of red pens is 18 of the 40 black pens. Thus, the number of red pens is 40(18), or 5 .

Choice B is incorrect. This is the number of black pens in the box for every red pen.

Choice C is incorrect. This is the number of black pens in the box.

Choice D is incorrect. This is the number of red pens in the box if the ratio of black pens to red pens is 1 to 8 .

Question 46 46 of 368 selected Percentages H
Year Subscriptions
sold
2012 5,600
2013 5,880

The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?

  1. 6,020

  2. 6,027

  3. 6,440

  4. 6,468

Show Answer Correct Answer: B

Choice B is correct. The percent increase from 2012 to 2013 was the fraction with numerator 5,880 minus 5,600, and denominator 5,600, equals 0 point 0 5, or 5%. Since the percent increase from 2012 to 2013 was estimated to be double the percent increase from 2013 to 2014, the percent increase from 2013 to 2014 was expected to be 2.5%.
Therefore, the number of subscriptions sold in 2014 is expected to be the number of subscriptions sold in 2013 multiplied by 1 plus 0 point 0 2 5, or 5,880 times 1 point 0 2 5, equals 6,027.

Choice A is incorrect and is the result of adding half of the value of the increase from 2012 to 2013 to the 2013 result. Choice C is incorrect and is the result adding twice the value of the increase from 2012 to 2013 to the 2013 result. Choice D is incorrect and is the result of interpreting the percent increase from 2013 to 2014 as double the percent increase from 2012 to 2013.

Question 47 47 of 368 selected Inference From Sample Statistics And Margin Of Error E

A city has 50 city council members. A reporter polled a random sample of 20 city council members and found that 6 of those polled supported a specific bill. Based on the sample, which of the following is the best estimate of the number of city council members in the city who support the bill?

  1. 6
  2. 9
  3. 15
  4. 30
Show Answer Correct Answer: C

Choice C is correct. Because a random sample of the city council was polled, the proportion of the sample who supported the bill is expected to be approximately equal to the proportion of the total city council who supports the bill. Since 6 of the 20 polled, or 30%, supported the bill, it can be estimated that 50 times 0 point 3, or 15, city council members support the bill.

Choice A is incorrect. This is the number of city council members in the sample who supported the bill. Choice B is incorrect and may result from a computational error. Choice D is incorrect. This is the number of city council members in the sample of city council members who were not polled.

Question 48 48 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

Pure beeswax has a density of 0.555 ounce per cubic inch. An online company sells pure beeswax at a price of $8.00 per ounce. What is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company?

Show Answer

The correct answer is 4.44. The selling price, in dollars per cubic inch, is found by multiplying the density, in ounces per cubic inch, by the unit price, in dollars per ounce: open parenthesis, 0 point 5 5 5 ounce, over 1 cubic inch, close parenthesis, times, open parenthesis, 8 dollars, over 1 ounce, close parenthesis yields 4 point 4 4 dollars over 1 cubic inch . Thus, the selling price, in dollars per cubic inch, is 4.44.

Question 49 49 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

The population density of Worthington is 290 people per square mile. Worthington has a population of 92,800 people. What is the area, in square miles, of Worthington?

  1. 102,400

  2. 93,090

  3. 320

  4. 32

Show Answer Correct Answer: C

Choice C is correct. It’s given that the population density of Worthington is 290 people per square mile and Worthington has a population of 92,800 people. Therefore, the area of Worthington is 92,800 people(1 square mile290 people), which is equivalent to 92,800 square miles290, or 320 square miles.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 50 50 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

Data set A consists of the 5 numbers: 72, 73, 73, 76, and 76. Data set B consists of the 5 numbers: 61, 64, 74, 85, and x.

Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of x ?

  1. 77

  2. 85

  3. 86

  4. 95

Show Answer Correct Answer: C

Choice C is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is the fraction with numerator 72, plus 73, plus 73, plus 76, plus 76, and denominator 5, which simplifies to 74. The mean of data set B is represented by the equation the fraction with numerator 61, plus 64, plus 74, plus 85, plus x, and denominator 5, or the fraction with numerator 284 plus x, and denominator 5. It’s given that the mean of data set A is equal to the mean of data set B. Therefore, the equation 74 equals, the fraction with numerator 284 plus x, and denominator 5 can be used to solve for x. Multiplying both sides of this equation by 5 yields 370 equals, 284 plus x. Subtracting 284 from both sides of this equation yields 86 equals x.

Choices A, B, and D are incorrect and may result from calculation errors.

Question 51 51 of 368 selected Percentages H

The figure presents a line graph. The horizontal axis is labeled “Year,” and the years 2003 through 2015 are indicated. The vertical axis is labeled “Annual snowfall, in inches,” and the numbers 0 through 60, in increments of 10, are indicated. There are 13 points indicated on the graph. The data represented by the 13 points are as follows. Note that all values are approximate.  Year, 2003. Number of inches, 40. Year, 2004. Number of inches, 12. Year, 2005. Number of inches, 13. Year, 2006. Number of inches, 14. Year, 2007. Number of inches, 10. Year, 2008. Number of inches, 5. Year, 2009. Number of inches, 8. Year, 2010. Number of inches, 56. Year, 2011. Number of inches, 10. Year, 2012. Number of inches, 3. Year, 2013. Number of inches, 4. Year, 2014. Number of inches, 32. Year, 2015. Number of inches, 19.


The line graph shows the total amount of snow, in inches, recorded each year in Washington, DC, from 2003 to 2015. If p percent is the percent decrease in the annual snowfall from 2003 to 2007, what is the value of p ?

Show Answer

The correct answer is 75. The percent decrease between two values is found by dividing the difference between the two values by the original value and multiplying by 100. The line graph shows that the annual snowfall in 2003 was 40 inches, and the annual snowfall in 2007 was 10 inches. Therefore, the percent decrease in the annual snowfall from 2003 to 2007 is open parenthesis, the fraction with numerator 40 minus 10, and denominator 40, close parenthesis, times 100, or 75. It’s given that this is equivalent to p percent, so the value of p is 75.

Question 52 52 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A wind turbine completes 900 revolutions in 50 minutes. At this rate, how many revolutions per minute does this turbine complete?

  1. 18

  2. 850

  3. 950

  4. 1,400

Show Answer Correct Answer: A

Choice A is correct. Dividing the number of revolutions by the number of minutes gives the number of revolutions the turbine completes per minute. It’s given that the wind turbine completes 900 revolutions in 50 minutes. Therefore, at this rate, this turbine completes 90050, or 18 , revolutions per minute.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 53 53 of 368 selected Two-Variable Data: Models And Scatterplots E

The line graph shows the percent of cars for sale at a used car lot on a given day by model year.

  • The line graph:
    • Begins at 2010, 12%
    • Remains level to 2011, 12%
    • Remains level to 2012, 12%
    • Falls sharply to 2013, 8%
    • Falls sharply to 2014, 4%
    • Rises sharply to 2015, 9%
    • Rises gradually to 2016, 10%
    • Remains level to 2017, 10%
    • Rises gradually to 2018, 11%
    • Remains level to 2019, 11%

For what model year is the percent of cars for sale the smallest?

  1. 2012

  2. 2013

  3. 2014

  4. 2015

Show Answer Correct Answer: C

Choice C is correct. For the given line graph, the percent of cars for sale at a used car lot on a given day is represented on the vertical axis. The percent of cars for sale is the smallest when the height of the line graph is the lowest. The lowest height of the line graph occurs for cars with a model year of 2014.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.

Question 54 54 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

The number of raccoons in a 131 -square-mile area is estimated to be 2,358 . What is the estimated population density, in raccoons per square mile, of this area?

  1. 18

  2. 131

  3. 149

  4. 2,376

Show Answer Correct Answer: A

Choice A is correct. It’s given that there are 2,358 raccoons in a 131 -square-mile area. The estimated population density, in raccoons per square mile, is the estimated number of raccoons divided by the number of square miles. Therefore, the estimated population density of this area is 2,358 raccoons131 square miles, or 18 raccoons per square mile.

Choice B is incorrect. This is the number of square miles in the area, not the estimated number of raccoons per square mile in this area.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 55 55 of 368 selected Probability And Conditional Probability E

A survey taken by 1,000 students at a school asked whether they played school sports. The table below summarizes all 1,000 responses from the students surveyed.

The figure presents a 3-column table with 2 rows of data. The first column has no heading. The heading for the second column is “Males,” and the heading for the third column is “Females.” The data are as follows. 

Row 1. Play a school sport: Males, 312; Females, 220.
Row 2. Do not play a school sport: Males, question mark; Females, 216.

How many of the males surveyed responded that they do not play a school sport?

  1. 109

  2. 252

  3. 468

  4. 688

Show Answer Correct Answer: B

Choice B is correct. The table summarizes all 1,000 responses from the students surveyed. If 312 are males who play a sport, 220 are females who play a sport, and 216 are females who do not play a sport, then 1,000 – 312 – 220 – 216 = 252 males who do not play a sport.

Choices A, C, and D are incorrect. If 109 males who do not play a sport responded, then the table summary would be 109 + 312 + 220 + 216 = 857 total student responses rather than 1,000. If 468 males who do not play a sport responded, then the table summary would be 468 + 312 + 220 + 216 = 1,216 total student responses rather than 1,000. If 688 males who do not play a sport responded, then the table summary would be 688 + 312 + 220 + 216 = 1,436 total student responses rather than 1,000.
 

Question 56 56 of 368 selected Inference From Sample Statistics And Margin Of Error M

A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?

  1. The majority of all fish in the pond weigh less than 2 pounds.

  2. The average weight of all fish in the pond is approximately 2 pounds.

  3. Approximately 30% of all fish in the pond weigh more than 2 pounds.

  4. Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

Show Answer Correct Answer: D

Choice D is correct. The sample of 150 largemouth bass was selected at random from all the largemouth bass in the pond, and since 30% of the fish in the sample weighed more than 2 pounds, it can be concluded that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

Choices A, B, and C are incorrect. Since the sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds, this result can be generalized only to largemouth bass in the pond, not to all fish in the pond.

Question 57 57 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the relationship between two variables, x and y .

  • The scatterplot has 8 data points.
  • The data points are in an exponential pattern trending up from left to right. 
  • The data points have the following approximate coordinates:
    • (0.3 comma 75)
    • (1.9 comma 200)
    • (2.6 comma 183)
    • (3.5 comma 898)
    • (4.2 comma 802)
    • (5.1 comma 2,173)
    • (5.7 comma 2,658)
    • (6.4 comma 4,766)

Which of the following graphs shows the most appropriate model for the data?

    • The scatterplot has 8 data points.
    • The data points are in an exponential pattern trending up from left to right. 
    • A line of best fit is shown:
      • The line of best fit slants up from left to right.
      • 0 points are touching the line of best fit.
      • 1 point is above the line of best fit.
      • 7 points are below the line of best fit.
      • The line of best fit passes through the following approximate coordinates:
        • (0 comma 0)
        • (6 comma 4,290)

    • The scatterplot has 8 data points.
    • The data points are in an exponential pattern trending up from left to right. 
    • A line of best fit is shown:
      • The line of best fit slants down from left to right.
      • 0 points are touching the line of best fit.
      • 3 points are above the line of best fit.
      • 5 points are below the line of best fit.
      • The line of best fit passes through the following coordinates:
        • (0 comma 5,000)
        • (6 comma 710)

    • The scatterplot has 8 data points.
    • The data points are in an exponential pattern trending up from left to right. 
    • A curve of best fit is shown:
      • The curve of best fit trends up from left to right.
      • 0 points are touching the curve of best fit.
      • 0 points are above the curve of best fit.
      • 8 points are below the curve of best fit.
      • The curve of best fit passes through the following coordinates:
        • (0 comma 1,055)
        • (4 comma 1,880)
        • (6 comma 4,520)

    • The scatterplot has 8 data points.
    • The data points are in an exponential pattern trending up from left to right. 
    • A curve of best fit is shown:
      • The curve of best fit trends up from left to right.
      • 2 points are touching the curve of best fit.
      • 3 points are above the curve of best fit.
      • 3 points are below the curve of best fit.
      • The curve of best fit passes through the following approximate coordinates:
        • (0 comma 51)
        • (4 comma 851)
        • (6 comma 3,472)

Show Answer Correct Answer: D

Choice D is correct. An appropriate model should follow the trend of the data points and should have data points both above and below the model. The scatterplot shows that the data points have an increasing trend that is curved. Therefore, an appropriate model should be an increasing curve with data points both above and below the model. Of the given choices, only the model in choice D is an increasing curve with data points both above and below the model.

Choice A is incorrect. Since the trend of the data points isn't linear, a line isn't the most appropriate model for the data.

Choice B is incorrect. Since the trend of the data points is increasing and isn't linear, a decreasing line isn't the most appropriate model for the data.

Choice C is incorrect. All the data points are below the model shown in this graph.

Question 58 58 of 368 selected Probability And Conditional Probability H

 

 Blood type   
Rhesus factorABABO
plus339337
minus721x

Human blood can be classified into four common blood types—A, B, AB, and O. It is also characterized by the presence open parenthesis, plus, close parenthesis or absence open parenthesis, minus, close parenthesis of the rhesus factor. The table above shows the distribution of blood type and rhesus factor for a group of people. If one of these people who is rhesus negative open parenthesis, minus, close parenthesis is chosen at random, the probability that the person has blood type B is one ninth . What is the value of x ?

Show Answer

The correct answer is 8. In this group, one ninth of the people who are rhesus negative have blood type B. The total number of people who are rhesus negative in the group is 7 plus 2, plus 1, plus x, and there are 2 people who are rhesus negative with blood type B. Therefore, the fraction with numerator 2, and denominator, 7 plus 2, plus 1, plus x, end fraction, equals one ninth. Combining like terms on the left-hand side of the equation yields the fraction with numerator 2, and denominator, 10 plus x, end fraction, equals one ninth. Multiplying both sides of this equation by 9 yields the fraction with numerator 18, and denominator, 10 plus x, end fraction, equals 1, and multiplying both sides of this equation by open parenthesis, 10 plus x, close parenthesis yields 18 equals, 10 plus x. Subtracting 10 from both sides of this equation yields 8 equals x.

Question 59 59 of 368 selected Probability And Conditional Probability M

The table below shows the number of state parks in a certain state that contain camping facilities and bicycle paths.

 Has bicycle pathsDoes not have bicycle paths
Has camping facilities205
Does not have camping facilities84

If one of these state parks is selected at random, what is the probability that it has camping facilities but does not have bicycle paths?

  1. 5 over 37

  2. 5 over 25

  3. 8 over 28

  4. 5 over 9

Show Answer Correct Answer: A

Choice A is correct. The total number of state parks in the state is 20, plus 5, plus 8, plus 4, equals 37. According to the table, 5 of these have camping facilities but not bicycle paths. Therefore, if a state park is selected at random, the probability that it has camping facilities but not bicycle paths is 5 over 37.

Choice B is incorrect. This is the probability that a state park selected at random from the state parks with camping facilities does not have bicycle paths. Choice C is incorrect. This is the probability that a state park selected at random from the state parks with bicycle paths does not have camping facilities. Choice D is incorrect. This is the probability that a state park selected at random from the state parks without bicycle paths does have camping facilities.

 

Question 60 60 of 368 selected Probability And Conditional Probability M

In a bag, there are 7 red, 4 white, 33 blue, and 33 yellow cubes. If one of these cubes is selected at random, what is the probability of selecting a cube that is neither blue nor yellow?

  1. 67

  2. 711

  3. 13

  4. 17

Show Answer Correct Answer: D

Choice D is correct. It’s given that there are 7 red, 4 white, 33 blue, and 33 yellow cubes in the bag. Therefore, there are a total of 7+4+33+33, or 77 , cubes in the bag. If the cube is neither blue nor yellow, then it must be either red or white. Therefore, the probability of selecting a cube that is neither blue nor yellow is equivalent to the probability of selecting a cube that is either red or white. If one of these cubes is selected at random, the probability of selecting a cube that is either red or white is equal to the sum of the number of red cubes and white cubes divided by the total number of cubes in the bag. There are 7 red cubes, 4 white cubes, and 77 total cubes in the bag. Therefore, the probability of selecting a red or white cube is 7+477, which is equivalent to 1177, or 1 7 . Thus, if one cube is selected at random, the probability of selecting a cube that is neither blue nor yellow is 1 7 .

Choice A is incorrect. This is the probability of selecting a cube that is either blue or yellow, rather than the probability of selecting a cube that is neither blue nor yellow.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 61 61 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

For a school fund-raiser, 10 students sold a total of 90 boxes of cookies. Which of the following can be calculated from this information?

  1. The average number of boxes sold per student

  2. The median number of boxes sold per student

  3. The greatest number of boxes sold by one student

  4. The least number of boxes sold by one student

Show Answer Correct Answer: A

Choice A is correct. The average can be found by dividing the total number of boxes sold by the number of students, which is the fraction 90 over 10, equals 9.

Choices B, C, and D are incorrect. Each results from choosing measures that require the results of individual students, which are not given.

Question 62 62 of 368 selected Two-Variable Data: Models And Scatterplots M

  • In quadrant 1:
    • The curve begins at point (0 comma 1).
    • The curve rises sharply to point (2 comma 6).
    • The curve rises gradually to point (4 comma 7).
    • The curve rises gradually to point (6 comma 8).
    • The curve rises sharply and ends at point (8 comma 10).

The graph shows the momentum y , in newton-seconds, of an object x seconds after the object started moving, for 0x8. What is the average rate of change, in newton-seconds per second, in the momentum of the object from x = 2 to x = 6 ?

Show Answer Correct Answer: .5, 1/2

The correct answer is 12. For the graph shown, x represents time, in seconds, and y represents momentum, in newton-seconds. Therefore, the average rate of change, in newton-seconds per second, in the momentum of the object between two x-values is the difference in the corresponding y-values divided by the difference in the x-values. The graph shows that at x = 2 , the corresponding y-value is 6 . The graph also shows that at x = 6 , the corresponding y-value is 8 . It follows that the average rate of change, in newton-seconds per second, from x = 2 to x = 6 is 8-66-2, which is equivalent to 24, or 12. Note that 1/2 and .5 are examples of ways to enter a correct answer.

Question 63 63 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

The results of two independent surveys are shown in the table below.

Men's Height
Group Sample size Mean (centimeters) Standard deviation (centimeters)
A 2,500 186 12.5
B 2,500 186 19.1

Which statement is true based on the table?

  1. The Group A data set was identical to the Group B data set.

  2. Group B contained the tallest participant.

  3. The heights of the men in Group B had a larger spread than the heights of the men in Group A.

  4. The median height of Group B is larger than the median height of Group A.

Show Answer Correct Answer: C

Choice C is correct. Standard deviation is a measure of spread, so data sets with larger standard deviations tend to have larger spread. The standard deviation of the heights of the men in Group B is larger than the standard deviation of the heights of the men in Group A. Therefore, the heights of the men in Group B had a larger spread than the heights of the men in Group A.

Choice A is incorrect. If two data sets are identical, they will have equivalent means and equivalent standard deviations. Since the two data sets have different standard deviations, they cannot be identical. Choice B is incorrect. Without knowing the maximum value for each data set, it’s impossible to know which group contained the tallest participant. Choice D is incorrect. Since the means of the two groups are equivalent, the medians could also be the same or could be different, but it's impossible to tell from the given information.

Question 64 64 of 368 selected Percentages H

The positive number a is 230% of the number b , and a is 60% of the number c . If c is p% of b , which of the following is closest to the value of p ?

  1. 138

  2. 217

  3. 283

  4. 383

Show Answer Correct Answer: D

Choice D is correct. It's given that a is 230% of b . It follows that a=230100b. It's also given that a is 60% of c . It follows that a=60100c. Since a=230100b and a=60100c, it follows that 230100b=60100c. Multiplying each side of this equation by 10060 yields 236b=c. If c is p% of b , then c=p100b. It follows that 23 6 = p 100 . Multiplying each side of this equation by 100 yields 2,3006=p. It follows that the value of p is approximately 383.33 . Therefore, of the given choices, 383 is closest to the value of p .

Choice A is incorrect. This is closest to the value of p if b is 230% of a , rather than if a is 230% of b , and if b is p% of c , rather than if c is p% of b .

Choice B is incorrect. This is closest to the value of p if a is 230% greater than b , rather than 230% of b .

Choice C is incorrect. This is closest to the value of p if c is p% greater than b , rather than p% of b .

Question 65 65 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

The bar graph shows the distribution of the number of walnuts per container for 20 containers at a grocery store.

876543210Frequency75767778Number of walnuts per container
  • The Frequency data for the 4 bars are as follows:
    • 75 walnuts per container: 2
    • 76 walnuts per container: 5
    • 77 walnuts per container: 6
    • 78 walnuts per container: 7

How many of these containers of walnuts contain exactly 78 walnuts?

  1. 2

  2. 7

  3. 20

  4. 78

Show Answer Correct Answer: B

Choice B is correct. The height of each bar in the graph shown represents the number of containers that contain the number of walnuts specified at the bottom of the bar. The bar for 78 walnuts has a height of 7 . Therefore, 7 of these containers of walnuts contain exactly 78 walnuts.

Choice A is incorrect. This is the number of containers that contain exactly 75 walnuts, not 78 walnuts.

Choice C is incorrect. This is the total number of containers of walnuts represented in the bar graph, not the number that contain exactly 78 walnuts.

Choice D is incorrect. This is the number of walnuts in a container that contains exactly 78 walnuts, not the number of containers that contain exactly 78 walnuts.

Question 66 66 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

15, 14, 18, 17, x

The mean and the median of the five numbers above are equal. Which of the following is NOT a possible value of ?

  1. 6

  2. 11

  3. 16

  4. 21

Show Answer Correct Answer: A

Choice A is correct. If x is 6, then the five numbers in the given list are 15, 14, 18, 17, 6. The mean of these five numbers is the sum of all the values divided by the number of values, or the fraction with numerator 15 plus 14, plus 18, plus 17, plus 6, and denominator 5, end fraction, equals, 70 over 5, which equals 14. The median of these five numbers can be found by ordering the numbers from least to greatest and determining the middle value. When ordered from least to greatest, the numbers in the given list are 6, 14, 15, 17, 18, and the middle value is 15. Since the mean is 14 and the median is 15, the mean and median aren’t equal when x is 6.

Choices B, C, and D are incorrect. If any of these values is substituted for x, the mean and median of the data set would be equal.

 

Question 67 67 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

  • The Frequency data for the 4 bars are as follows:
    • blue: 27
    • green: 70
    • red: 33
    • yellow: 43

 

A data set consists of 173 colors. The bar graph shows the number of times each color appears in the data set. Which color appears 70 times?

  1. Blue

  2. Green

  3. Red

  4. Yellow

Show Answer Correct Answer: B

Choice B is correct. It's given that a data set consists of 173 colors and the bar graph shows the number of times each color appears in the data set. Therefore, for each color specified at the bottom of the bar, the frequency corresponds to the number of times that color appears in the data set. The color that appears 70 times in the data set has a frequency of 70 on the bar graph. Since the bar with a frequency of 70 corresponds to green, green is the color that appears 70 times.

Choice A is incorrect. The color blue appears about 27 times, not 70 times.

Choice C is incorrect. The color red appears about 33 times, not 70 times.

Choice D is incorrect. The color yellow appears about 43 times, not 70 times.

Question 68 68 of 368 selected Percentages E

What percentage of 300 is 75 ?

  1. 25 %

  2. 50 %

  3. 75 %

  4. 225 %

Show Answer Correct Answer: A

Choice A is correct. Let x represent the percentage of 300 that is 75 . This can be written as x100(300)=75, or 3 x = 75 . Dividing both sides of this equation by 3 yields x = 25 . Therefore, 25% of 300 is 75 .

Choice B is incorrect. 50% of 300 is 150 , not 75 .

Choice C is incorrect. 75% of 300 is 225 , not 75 .

Choice D is incorrect. 225% of 300 is 675 , not 75 .

Question 69 69 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

Data set A consists of 10 positive integers less than 60 . The list shown gives 9 of the integers from data set A.

43 , 45 , 44 , 43 , 38 , 39 , 40 , 46 , 40

The mean of these 9 integers is 42 . If the mean of data set A is an integer that is greater than 42 , what is the value of the largest integer from data set A?

Show Answer Correct Answer: 52

The correct answer is 52 . The mean of a data set is calculated by dividing the sum of the data values by the number of values. It’s given that data set A consists of 10 values, 9 of which are shown. Let x represent the 10th data value in data set A, which isn’t shown. The mean of data set A can be found using the expression 43+45+44+43+38+39+40+46+40+x10, or 378+x10. It’s given that the mean of the 9 values shown is 42 and that the mean of all 10 numbers is greater than 42 . Consequently, the 10th data value, x , is larger than 42 . It’s also given that the data values in data set A are positive integers less than 60 . Thus, 42<x<60. Finally, it’s given that the mean of data set A is an integer. This means that the sum of the 10 data values, 378+x, is divisible by 10 . Thus, 378+x must have a ones digit of 0 . It follows that x must have a ones digit of 2 . Since 42<x<60 and x has a ones digit of 2 , the only possible value of x is 52 . Since 52 is larger than any of the integers shown, the largest integer from data set A is 52 .

Question 70 70 of 368 selected Ratios, Rates, Proportional Relationships, And Units E
x y
1 4
3 12
5 20
40 k

In the table above, the ratio of y to x for each ordered pair is constant. What is the value of k ?

  1. 28

  2. 36

  3. 80

  4. 160

Show Answer Correct Answer: D

Choice D is correct. Since the ratio of y to x is constant for each ordered pair in the table, the first row can be used to determine that the ratio of y to x is 4 to 1. The proportion 4 over 1, equals k over 40 can be used to solve for k. Multiplying each side of the equation by 40 yields 160 equals k.

Choice A is incorrect. This is the value of y when the value of x is 7, not 40. Choice B is incorrect and may result from subtracting 4 from 40 instead of multiplying 40 by 4. Choice C is incorrect and may result from incorrectly setting up the proportion.

Question 71 71 of 368 selected Percentages E

The cost of a certain shirt is $20 before a 5% sales tax is added. What is the total cost, including sales tax, to purchase the shirt?

  1. $20.05

  2. $20.50

  3. $21.00

  4. $25.00

Show Answer Correct Answer: C

Choice C is correct. The total cost to purchase the shirt is the $20 cost of the shirt plus the 5% sales tax. The value of the 5% sales tax on the $20 shirt is equivalent to0 point 0 5 times 20 dollars, or $1. Therefore, the total cost to purchase the shirt is 20 dollars plus 1 dollar, or $21.

Choice A is incorrect and may result from neglecting to multiply by $20 when finding the value of the sales tax. Choice B is incorrect and may result from dividing by 10, instead of by 100, and then neglecting to multiply by $20 when finding the sales tax. Choice D is incorrect and may result from interpreting the sales tax of 5% as $5.

Question 72 72 of 368 selected Two-Variable Data: Models And Scatterplots M

In the given scatterplot, a line of best fit for the data is shown.

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending down from left to right.
  • A line of best fit is shown:
  • The line of best fit slants down from left to right.
    • 5 points are touching the line of best fit.
    • 2 points are above the line of best fit.
    • 3 points are below the line of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (1 comma 7)
      • (4 comma 5)
      • (10 comma 1)

Which of the following is closest to the slope of this line of best fit?

  1. 7

  2. 0.7

  3. -0.7

  4. -7

Show Answer Correct Answer: C

Choice C is correct. A line of best fit is shown in the scatterplot such that as the value of x increases, the value of y decreases. It follows that the slope of the line of best fit shown is negative. The slope of a line in the xy-plane that passes through the points (x1,y1) and (x2,y2) can be calculated as y2-y1x2-x1. The line of best fit shown passes approximately through the points (0,8) and (10,1). Substituting (0,8) for (x1,y1) and (10,1) for (x2,y2) in y2-y1x2-x1 yields the slope of the line being approximately 1-810-0, which is equivalent to -710, or -0.7. Therefore, of the given choices, -0.7 is the closest to the slope of this line of best fit.

Choice A is incorrect. The line of best fit shown has a negative slope, not a positive slope.

Choice B is incorrect. The line of best fit shown has a negative slope, not a positive slope.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 73 73 of 368 selected Inference From Sample Statistics And Margin Of Error M

A park ranger asked a random sample of visitors how far they hiked during their visit. Based on the responses, the estimated mean was found to be 4.5 miles, with an associated margin of error of 0.5 miles. Which of the following is the best conclusion from these data?

  1. It is likely that all visitors hiked between 4 and 5 miles.

  2. It is likely that most visitors hiked exactly 4.5 miles.

  3. It is not possible that any visitor hiked less than 3 miles.

  4. It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.

Show Answer Correct Answer: D

Choice D is correct. The given estimated mean has an associated margin of error because from sample data, the population mean can’t be determined precisely. Rather, from the sample mean, an interval can be determined within which it’s plausible that the population’s mean is likely to lie. Since the estimated mean is 4.5 miles with an associated margin of error of 0.5 miles, it follows that between 4 point 5 minus 0 point 5 miles and 4 point 5 plus 0 point 5 miles, or between 4 and 5 miles, is plausibly the mean distance hiked for all visitors.

Choices A, B, and C are incorrect. Based on the estimated mean, no determination can be made about the number of miles hiked for all visitors to the park.

Question 74 74 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

The ratio of the length of line segment XY to the length of line segment ZV is 6 to 1 . If the length of line segment XY is 102 inches, what is the length, in inches, of line segment ZV?

  1. 17

  2. 96

  3. 102

  4. 612

Show Answer Correct Answer: A

Choice A is correct. It’s given that the ratio of the length of line segment XY to the length of line segment ZV is 6 to 1 , which means XYZV=61. It’s given that the length of line segment XY is 102 inches. If the length, in inches, of line segment ZV is represented by l, the value of l can be calculated by solving the equation 102l=61, or 102l=6. Multiplying each side of this equation by l yields 102=6l. Dividing each side of this equation by 6 yields 17=l. Therefore, the length of line segment ZV is 17 inches.

Choice B is incorrect. This is the length, in inches, of line segment ZV if the length of line segment XY is 576 , not 102 , inches.

Choice C is incorrect. This is the length, in inches, of line segment XY, not line segment ZV.

Choice D is incorrect. This is the length, in inches, of line segment ZV if the ratio of the length of line segment XY to the length of line segment ZV is 1 to 6 , not 6 to 1 .

Question 75 75 of 368 selected Two-Variable Data: Models And Scatterplots H

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 11.9)
      • (12 comma 30.3)
      • (20 comma 42.6)

The scatterplot shows the relationship between two variables, x and y , for data set E. A line of best fit is shown. Data set F is created by multiplying the y-coordinate of each data point from data set E by 3.9 . Which of the following could be an equation of a line of best fit for data set F?

  1. y=46.8+5.9x

  2. y=46.8+1.5x

  3. y=12+5.9x

  4. y=12+1.5x

Show Answer Correct Answer: A

Choice A is correct. An equation of a line of best fit for data set F can be written in the form y=a+bx, where a is the y-coordinate of the y-intercept of the line of best fit and b is the slope. The line of best fit shown for data set E has a y-intercept at approximately (0,12). It's given that data set F is created by multiplying the y-coordinate of each data point from data set E by 3.9 . It follows that a line of best fit for data set F has a y-intercept at approximately (0,12(3.9)), or (0,46.8). Therefore, the value of a is approximately 46.8 . The slope of a line that passes through points (x1,y1) and (x2,y2) can be calculated as y2-y1x2-x1. Since the line of best fit shown for data set E passes approximately through the point (12,30), it follows that a line of best fit for data set F passes approximately through the point (12,30(3.9)), or (12,117). Substituting (0,46.8) and (12,117) for (x1,y1) and (x2,y2), respectively, in y2-y1x2-x1 yields 117-46.812-0, which is equivalent to 70.212, or 5.85 . Therefore, the value of b is approximately 5.85 , or approximately 5.9 . Thus, y=46.8+5.9x could be an equation of a line of best fit for data set F.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This could be an equation of a line of best fit for data set E, not data set F.

Question 76 76 of 368 selected Percentages M

For the finale of a TV show, viewers could use either social media or a text message to vote for their favorite of two contestants. The contestant receiving more than 50% of the vote won. An estimated 10% of the viewers voted, and 30% of the votes were cast on social media. Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, which of the following is an accurate conclusion?

  1. If all viewers had voted, Contestant 2 would have won.

  2. Viewers voting by social media were likely to be younger than viewers voting by text message.

  3. If all viewers who voted had voted by social media instead of by text message, Contestant 2 would have won.

  4. Viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.

Show Answer Correct Answer: D

Choice D is correct. It is given that Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.

Choices A, B, and C are incorrect. There is not enough information about the viewers to reach these conclusions.

Question 77 77 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H
Value Data set A frequency Data set B frequency
30 2 9
34 4 7
38 5 5
42 7 4
46 9 2

Data set A and data set B each consist of 27 values. The table shows the frequencies of the values for each data set. Which of the following statements best compares the means of the two data sets?

  1. The mean of data set A is greater than the mean of data set B.

  2. The mean of data set A is less than the mean of data set B.

  3. The mean of data set A is equal to the mean of data set B.

  4. There is not enough information to compare the means of the data sets.

Show Answer Correct Answer: A

Choice A is correct. The mean value of a data set is the sum of the values of the data set divided by the number of values in the data set. When a data set is represented in a frequency table, the sum of the values in the data set is the sum of the products of each value and its frequency. For data set A, the sum of products of each value and its frequency is 30(2)+34(4)+38(5)+42(7)+46(9), or 1,094. It's given that there are 27 values in data set A. Therefore, the mean of data set A is 1,09427, or approximately 40.52. Similarly, the mean of data B is 95827, or approximately 35.48. Therefore, the mean of data set A is greater than the mean of data set B.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 78 78 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

The ratio x to y is equivalent to the ratio 9 to 5 . If the value of x is 162 , what is the value of y ?

Show Answer Correct Answer: 90

The correct answer is 90 . It’s given that the ratio of x to y is equivalent to the ratio 9 to 5 . It follows that xy=95. Multiplying each side of this equation by 5 y yields (5y)xy=9(5y)5, or 5x=9y. Dividing each side of this equation by 9 yields 5x9=y. Substituting 162 for x in this equation yields 5(162)9=y, which is equivalent to 8109=y, or 90=y. Therefore, if the value of x is 162 , the value of y is 90 .

Question 79 79 of 368 selected Two-Variable Data: Models And Scatterplots M

Which of the following is true about the values of 2 to the x power and 2 x plus 2 for x greater than 0?

  1. For all x greater than 0, it is true that 2 to the x power, is less than 2 x plus 2.

  2. For all x greater than 0, it is true that 2 to the x power, is greater than 2 x plus 2.

  3. There is a constant c such that if 0 is less than x, which is less than c, then 2 to the x power, is less than 2 x plus 2, but if x is greater than c, then 2 to the x power, is greater than 2 x plus 2.

  4. There is a constant c such that if 0 is less than x, which is less than c, then 2 to the x power, is greater than 2 x plus 2, but if x is greater than c, then 2 to the x power, is less than 2 x plus 2.

Show Answer Correct Answer: C

Choice C is correct. At x equals 0, the value of 2 raised to the x power is less than the value of 2 x plus 2, where 2 to the 0 power is less than, 2 times 0, plus 2, which is equivalent to 1 is less than 2 . As the value of x increases, the value of 2 raised to the x power remains less than the value of 2 x plus 2 until x equals 3, which is when the two values are equal: 2 cubed equals, 2 times 3, plus 2, which is equivalent to 8 is equal to 8. Then, for x greater than 3, the value of 2 raised to the x power is greater than the value of 2 x plus 2. So there is a constant, 3, such that when 0 is less than x, which is less than 3, then 2 raised to the x power is less than, 2 x plus 2, but when x is greater than 3, then 2 raised to the x power is greater than, 2 x plus 2.

Choice A is incorrect because 2 raised to the x power is greater than, 2 x plus 2 when x is greater than 3. Choice B is incorrect because 2 raised to the x power is less than, 2 x plus 2 when 0 is less than x, which is less than 3. Choice D is incorrect because 2 raised to the x power is less than, 2 x plus 2 when 0 is less than x, which is less than 3 and 2 raised to the x power is greater than, 2 x plus 2 when x is greater than 3.

 

Question 80 80 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is created by adding 7 to each number in the original data set that is greater than the median and subtracting 7 from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

  1. Median

  2. Mean

  3. Sum of the numbers

  4. Standard deviation

Show Answer Correct Answer: D

Choice D is correct. When a data set has an odd number of elements, the median can be found by ordering the values from least to greatest and determining the middle value. Out of the 27 different numbers in this data set, 13 numbers are below the median, one number is exactly 33, and 13 numbers are above the median. When 7 is subtracted from each number below the median and added to each number above the median, the data spread out from the median. Since the median of this data set, 33, is equivalent to the mean of the data set, the data also spread out from the mean. Since standard deviation is a measure of how spread out the data are from the mean, a greater spread from the mean indicates an increased standard deviation.

Choice A is incorrect. All the numbers less than the median decrease and all the numbers greater than the median increase, but the median itself doesn’t change. Choices B and C are incorrect. The mean of a data set is found by dividing the sum of the values by the number of values. The net change from subtracting 7 from 13 numbers and adding 7 to 13 numbers is zero. Therefore, neither the mean nor the sum of the numbers changes.

 

Question 81 81 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

 

Species of treeGrowth factor
Red maple4.5
River birch3.5
Cottonwood2.0
Black walnut4.5
White birch5.0
American elm4.0
Pin oak3.0
Shagbark hickory7.5

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees. If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)

  1. 1.0

  2. 1.2

  3. 1.3

  4. 1.4

Show Answer Correct Answer: C

Choice C is correct. According to the given information, multiplying a tree species’ growth factor by the tree’s diameter is a method to approximate the age of the tree. A white birch with a diameter of 12 inches (or 1 foot) has a given growth factor of 5 and is approximately 60 years old. A pin oak with a diameter of 12 inches (or 1 foot) has a given growth factor of 3 and is approximately 36 years old. The diameters of the two trees 10 years from now can be found by dividing each tree’s age in 10 years, 70 years, and 46 years, by its respective growth factor. This yields 14 inches and 15 and one third inches. The difference between 15 and one third and 14 is 1 and one third, or approximately 1.3 inches.

Alternate approach: Since a white birch has a growth factor of 5, the age increases at a rate of 5 years per inch or, equivalently, the diameter increases at a rate of one fifth of an inch per year. Likewise, the pin oak has a growth factor of 3, so its diameter increases at a rate of one third of an inch per year. Thus, the pin oak grows two fifteenths of an inch per year more than the white birch. In 10 years it will grow two fifteenths times 10, equals four thirds of an inch more, which is approximately 1.3 inches.

Choices A, B, and D are incorrect and a result of incorrectly calculating the diameters of the two trees in 10 years.

Question 82 82 of 368 selected Two-Variable Data: Models And Scatterplots M

During a study, the temperature, in degrees Celsius (°C), of the air in a chamber was recorded to the nearest integer at certain times. The scatterplot shows the recorded temperature y , in °C, of the air in the chamber x minutes after the start of the study.

12345678x24681012141618202224262830yOTime (minutes)Temperature (°C)
  • The scatterplot has 7 data points.
  • The data points are in a linear pattern trending up from left to right.
  • The data points have the following coordinates:
    • (1 comma 4)
    • (2 comma 6)
    • (3 comma 12)
    • (4 comma 10)
    • (5 comma 14)
    • (6 comma 16)
    • (7 comma 24)

What was the average rate of change, in °C per minute, of the recorded temperature of the air in the chamber from x=5 to x=7?

Show Answer Correct Answer: 5

The correct answer is 5 . For the graph shown, x represents time, in minutes, and y represents temperature, in degrees Celsius (°C). Therefore, the average rate of change, in °C per minute, of the recorded temperature of the air in the chamber between two x-values is the difference in the corresponding y-values divided by the difference in the x-values. The graph shows that at x = 5 , the corresponding y-value is 14 . The graph also shows that at x = 7 , the corresponding y-value is 24 . It follows that the average rate of change, in °C per minute, from x = 5 to x = 7 is 24-147-5, which is equivalent to 102, or 5 .

Question 83 83 of 368 selected Probability And Conditional Probability E

The table gives the distribution of votes for a new school mascot and grade level for 80 students.

Mascot Grade level
Sixth Seventh Eighth Total
Badger 4 9 9 22
Lion 9 2 9 20
Longhorn 4 6 4 14
Tiger 6 9 9 24
Total 23 26 31 80

If one of these students is selected at random, what is the probability of selecting a student whose vote for new mascot was for a lion? 

  1. 1 9

  2. 1 5

  3. 1 4

  4. 2 3

Show Answer Correct Answer: C

Choice C is correct. If one of these students is selected at random, the probability of selecting a student whose vote for the new mascot was for a lion is given by the number of votes for a lion divided by the total number of votes. The given table indicates that the number of votes for a lion is 20 votes, and the total number of votes is 80 votes. The table gives the distribution of votes for 80 students, and the table shows a total of 80 votes were counted. It follows that each of the 80 students voted exactly once. Thus, the probability of selecting a student whose vote for the new mascot was for a lion is 2080, or 14.

Choice A is incorrect and may result from conceptual or computational errors.

Choice B is incorrect and may result from conceptual or computational errors.

Choice D is incorrect and may result from conceptual or computational errors.

Question 84 84 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

The ratio of t to u is 1 to 2, and t equals 10. What is the value of u ?

  1. 2

  2. 5

  3. 10

  4. 20

Show Answer Correct Answer: D

Choice D is correct. It’s given that the ratio of t to u is 1 to 2. Since t equals 10, it follows that the ratio of 10 to u is also 1 to 2. The relationship between these ratios can be represented by the proportion 10 over u, equals one half. Multiplying both sides of this equation by 2 and then by u yields 20 equals u.

Choice A is incorrect. This is the value of u when t equals 1. Choice B is incorrect. This would be the value of u if the ratio of t to u were 2 to 1. Choice C is incorrect. This is the value of t, not u.

Question 85 85 of 368 selected Probability And Conditional Probability H

A grove has 6 rows of birch trees and 5 rows of maple trees. Each row of birch trees has 8 trees 20 feet or taller and 6 trees shorter than 20 feet. Each row of maple trees has 9 trees 20 feet or taller and 7 trees shorter than 20 feet. A tree from one of these rows will be selected at random. What is the probability of selecting a maple tree, given that the tree is 20 feet or taller?

  1. 9 164

  2. 3 10

  3. 15 31

  4. 9 17

Show Answer Correct Answer: C

Choice C is correct. If a tree from one of these rows is selected at random, the probability of selecting a maple tree, given that the tree is 20 feet or taller, is equal to the number of maple trees that are 20 feet or taller divided by the total number of trees that are 20 feet or taller. It's given that there are 6 rows of birch trees, and each row of birch trees has 8 trees that are 20 feet or taller. This means that there are a total of 6(8), or 48 , birch trees that are 20 feet or taller. It's given that there are 5 rows of maple trees, and each row of maple trees has 9 trees that are 20 feet or taller. This means that there are a total of 5(9), or 45 , maple trees that are 20 feet or taller. It follows that there are a total of 48+45, or 93 , trees that are 20 feet or taller. Therefore, the probability of selecting a maple tree, given that the tree is 20 feet or taller, is 4593, or 15 31 .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 86 86 of 368 selected Percentages M

During the first month of sales, a company sold 1,300,000 units of a certain type of smartphone. During the same month, 15% of the units sold were returned. If sales and the return rate remain the same for each of the next 5 months, about how many units of this smartphone will be returned to the company during this 6-month period?

  1. 195,000

  2. 975,000

  3. 1,170,000

  4. 6,630,000

Show Answer Correct Answer: C

Choice C is correct. Of the 1,300,000 units sold during the first month, 15% were returned, so 1,300,000 times 0 point 1 5, equals 195,000 units were returned during the first month. If the units were sold and returned at the same rate for the next 5 months, then a total of 195,000 times 6, equals 1,170,000 smartphone units were returned during the 6-month period.

Choice A is incorrect. This is the number of units that were returned in 1 month. Choice B is incorrect. This is the number of units that were returned in 5 months. Choice D is incorrect. This is the number of units sold and not returned during the first 6 months.

Question 87 87 of 368 selected Percentages E

Last year, 200 students enrolled in an interior design program. This year, the number of students enrolled is 147% of last year’s number. How many students are enrolled in the interior design program this year?

  1. 247

  2. 294

  3. 347

  4. 394

Show Answer Correct Answer: B

Choice B is correct. It's given that the number of students enrolled in an interior design program this year is 147% of last year's number, which is 200 147% of 200 can be expressed as (147100)(200), or (1.47)(200), which is equivalent to 294 . Therefore, 294 students are enrolled in the interior design program this year.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 88 88 of 368 selected Two-Variable Data: Models And Scatterplots M

The scatterplot shows the relationship between two variables, x and y . A line of best fit is also shown.

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending down from left to right.
  • A line of best fit is shown:
    • The line of best fit slants down from left to right.
    • 2 points are touching the line of best fit.
    • 3 points are above the line of best fit.
    • 5 points are below the line of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 12.9)
      • (6 comma 8)
      • (12 comma 3.2)

Which of the following is closest to the slope of the line of best fit shown?

  1. -2.4

  2. -0.8

  3. 0.8

  4. 2.4

Show Answer Correct Answer: B

Choice B is correct. A line of best fit is shown in the scatterplot such that as the value of x increases, the value of y decreases. Thus, the slope of the line of best fit shown is negative. The slope of a line passing through two points, (x1,y1) and (x2,y2), can be calculated as y2-y1x2-x1. The line of best fit shown passes approximately through the points (1,12) and (11,4). Substituting (1,12) and (11,4) for (x1,y1) and (x2,y2), respectively, in y2-y1x2-x1 gives 4-1211-1, which is equivalent to -810, or -0.8. Therefore, of the given choices, -0.8 is closest to the slope of the line of best fit shown.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. The line of best fit shown has a negative slope, not a positive slope.

Choice D is incorrect. The line of best fit shown has a negative slope, not a positive slope.

Question 89 89 of 368 selected Probability And Conditional Probability E

Each rock in a collection of 70 rocks was classified as either igneous, metamorphic, or sedimentary, as shown in the frequency table.

Classification Frequency
igneous 10
metamorphic 33
sedimentary 27

If one of these rocks is selected at random, what is the probability of selecting a rock that is igneous?

  1. 1027

  2. 1033

  3. 1060

  4. 1070

Show Answer Correct Answer: D

Choice D is correct. If one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is equal to the number of igneous rocks in the collection divided by the total number of rocks in the collection. According to the table, there are 10 igneous rocks in the collection, and it's given that there's a total of 70 rocks in the collection. Therefore, if one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is 1070.

Choice A is incorrect. This is the number of igneous rocks in the collection divided by the number of sedimentary rocks in the collection, not divided by the total number of rocks in the collection.

Choice B is incorrect. This is the number of igneous rocks in the collection divided by the number of metamorphic rocks in the collection, not divided by the total number of rocks in the collection.

Choice C is incorrect. This is the number of igneous rocks in the collection divided by the number of rocks in the collection that aren't igneous, not divided by the total number of rocks in the collection.

Question 90 90 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

Five Eretmochelys imbricata, a type of sea turtle, each have a nest. The table shows an original data set of the number of eggs that each turtle laid in its nest.

Nest Number of eggs
A 149
B 144
C 148
D 136
E 139

A sixth nest with 121 eggs is added to create a new data set. Which of the following correctly compares the means of the two data sets?

  1. The mean of the original data set is greater than the mean of the new data set.

  2. The mean of the original data set is less than the mean of the new data set.

  3. The means of both data sets are equal.

  4. There is not enough information to compare the means.

Show Answer Correct Answer: A

Choice A is correct. It's given that the table shows an original data set of 5 values. It's also given that a sixth value is added to create a new data set. The new data set consists of the 5 values in the original data set and one additional value, 121 . Since the additional value, 121 , is less than any value in the original data set, the mean of the original data set is greater than the mean of the new data set.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 91 91 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments M

A survey was conducted using a sample of history professors selected at random from the California State Universities. The professors surveyed were asked to name the publishers of their current texts. What is the largest population to which the results of the survey can be generalized?

  1. All professors in the United States

  2. All history professors in the United States

  3. All history professors at all California State Universities

  4. All professors at all California State Universities

Show Answer Correct Answer: C

Choice C is correct. Selecting a sample at random when conducting a survey allows the results to be generalized to the population from which the sample was selected, but not beyond this population. In this situation, the population that the sample was selected from is history professors from the California State Universities. Therefore, the largest population to which the results of the survey can be generalized is all history professors at all California State Universities.

Choices A, B, and D are incorrect. Since the sample was selected at random from history professors from the California State Universities, the results of the survey can’t be generalized to all professors in the United States, all history professors in the United States, or all professors at all California State Universities. All three of these populations may use different texts and therefore may name different publishers.

 

Question 92 92 of 368 selected Percentages E

21 is 21% of what number?

  1. 0

  2. 1

  3. 42

  4. 100

Show Answer Correct Answer: D

Choice D is correct. Let x represent the number that 21 is 21% of. It follows that 21 x = 21 100 . Multiplying each side of this equation by x yields 21 = 21 x 100 . Multiplying each side of this equation by 100 yields 2,100 = 21 x . Dividing each side of this equation by 21 yields 100 = x . Therefore, 21 is 21% of 100 .

Choice A is incorrect. 21% of 0 is 0 , not 21 .

Choice B is incorrect. 21% of 1 is 0.21 , not 21 .

Choice C is incorrect. 21% of 42 is 8.82 , not 21 .

Question 93 93 of 368 selected Two-Variable Data: Models And Scatterplots H
The figure presents a scatterplot titled “Minimum Wage.” The x axis is labeled “Years since 1940,” and the integers 0 through 80, in increments of 10, are indicated. The y axis is labeled “Minimum wage, in dollars per hour,” and the integers 0 through 8 are indicated. There are 8 data points in the scatterplot, and the line of best fit is drawn. The line of best fit begins at the point representing 0 years since 1940, minimum wage 0 dollars per hour. It slants upward and to the right, and passes through the point representing 40 years since 1940, minimum wage 3 point 3 5 2 dollars, and the point representing 70 years since 1940, minimum wage 6 point 2 3 2 dollars

The scatterplot above shows the federal-mandated minimum wage every 10 years between 1940 and 2010. A line of best fit is shown, and its equation is y equals, 0 point 0 9 6 x, minus 0 point 4 8 8. What does the line of best fit predict about the increase in the minimum wage over the 70-year period?

  1. Each year between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.

  2. Each year between 1940 and 2010, the average increase in minimum wage was 0.49 dollars.

  3. Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.

  4. Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.488 dollars.

Show Answer Correct Answer: A

Choice A is correct. The given equation is in slope-intercept form, or y equals, m x plus b, where m is the value of the slope of the line of best fit. Therefore, the slope of the line of best fit is 0.096. From the definition of slope, it follows that an increase of 1 in the x-value corresponds to an increase of 0.096 in the y-value. Therefore, the line of best fit predicts that for each year between 1940 and 2010, the minimum wage will increase by 0.096 dollar per hour.

Choice B is incorrect and may result from using the y-coordinate of the y-intercept as the average increase, instead of the slope. Choice C is incorrect and may result from using the 10-year increments given on the x-axis to incorrectly interpret the slope of the line of best fit. Choice D is incorrect and may result from using the y-coordinate of the y-intercept as the average increase, instead of the slope, and from using the 10-year increments given on the x-axis to incorrectly interpret the slope of the line of best fit.

Question 94 94 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A special camera is used for underwater ocean research. When the camera is at a depth of 58 fathoms, what is the camera's depth in feet? (1 fathom=6 feet)

Show Answer Correct Answer: 348

The correct answer is 348 . It's given that 1 fathom is equivalent to 6 feet. Therefore, 58 fathoms is equivalent to (58 fathoms)(6 feet1 fathom), or 348 feet. Thus, when the camera is at a depth of 58 fathoms, the camera's depth, in feet, is 348 .

Question 95 95 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

A sample of oak has a density of 807  kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of 0.90 meters. To the nearest whole number, what is the mass, in kilograms, of this sample? 

  1. 588

  2. 726

  3. 897

  4. 1,107

Show Answer Correct Answer: A

Choice A is correct. It’s given that the sample is in the shape of a cube with edge lengths of 0.9 meters. Therefore, the volume of the sample is 0.903, or 0.729 , cubic meters. It’s also given that the sample has a density of 807 kilograms per 1 cubic meter. Therefore, the mass of this sample is 0.729 cubic meters(807 kilograms1 cubic meter), or 588.303 kilograms. Rounding this mass to the nearest whole number gives 588 kilograms. Therefore, to the nearest whole number, the mass, in kilograms, of this sample is 588 .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 96 96 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

73 , 74 , 75 , 77 , 79 , 82 , 84 , 85 , 91

What is the median of the data shown?

Show Answer Correct Answer: 79

The correct answer is 79 . The median of a data set with an odd number of values is the middle value of the set when the values are ordered from least to greatest. Because the given data set consists of nine values that are ordered from least to greatest, the median is the fifth value in the data set. Therefore, the median of the data shown is 79 .

Question 97 97 of 368 selected Two-Variable Data: Models And Scatterplots E
The figure presents a line graph. The horizontal axis is labeled “Graduating class year,” and the years 2000 through 2008, in increments of 2 years, are indicated. The vertical axis is labeled “Number of graduates who enrolled in college,” and the numbers 0 through 300, in increments of 50, are indicated. There are 7 data points indicated on the graph. The 7 data points represent the number of graduates from each of the classes from 2001 through 2007. The data represented by the 7 data points are as follows. Note that all numbers of graduates are approximate.

Year, 2001. Number of graduates, 225.
Year, 2002. Number of graduates, 220.
Year, 2003. Number of graduates, 240.
Year, 2004. Number of graduates, 260.
Year, 2005. Number of graduates, 280.
Year, 2006. Number of graduates, 255.
Year, 2007. Number of graduates, 275.

The line graph shows the number of graduates from the classes of 2001 through 2007 at a certain school who enrolled in college within 24 months of graduation. Of the following, which class had the fewest graduates who enrolled in college within 24 months of graduation?

  1. 2002

  2. 2004

  3. 2005

  4. 2007

Show Answer Correct Answer: A

Choice A is correct. The year with the fewest graduates who enrolled in college within 24 months of graduation is the point with the lowest value on the vertical axis. This occurs at 2002.

Choice B, C, and D are incorrect. The years 2004, 2005, and 2007 each had a greater number of graduates who enrolled in college within 24 months of graduation than did the year 2002.

Question 98 98 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

At a particular track meet, the ratio of coaches to athletes is 1 to 26 . If there are x coaches at the track meet, which of the following expressions represents the number of athletes at the track meet?

  1. x26

  2. 26x

  3. x+26

  4. 26x

Show Answer Correct Answer: B

Choice B is correct. It’s given that at a particular track meet, the ratio of coaches to athletes is 1 to 26 . If one number in a ratio is multiplied by a value, the other number must be multiplied by the same value in order to maintain the same ratio. If there are x coaches at the track meet, multiplying both numbers in the ratio by x yields 1(x) to 26(x), or x to 26 x . Therefore, the expression 26 x represents the number of athletes at the track meet.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 99 99 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

Show Answer

The correct answer is 25.4. The average speed is the total distance divided by the total time. The total distance is 11 miles and the total time is 26 minutes. Thus, the average speed is 11 over 26 miles per minute. The question asks for the average speed in miles per hour, and there are 60 minutes in an hour; converting miles per minute to miles per hour gives the following:

Average speed equals, the fraction 11 miles over 26 minutes, end fraction, times, the fraction 60 minutes over 1 hour, end fraction

 which equals, the fraction 660 over 26, end fraction, miles per hour

 which is approximately equal to 25 point 3 8 miles per hour

Therefore, to the nearest tenth of a mile per hour, the average speed of Paul Revere’s ride would have been 25.4 miles per hour. Note that 25.4 and 127/5 are examples of ways to enter a correct answer.

Question 100 100 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

How many yards are equivalent to 612 inches? (1 yard=36 inches)

  1. 0.059

  2. 17

  3. 576

  4. 22,032

Show Answer Correct Answer: B

Choice B is correct. It’s given that 1 yard=36 inches. Therefore, 612 inches is equivalent to 612 inches(1 yard36 inches), which can be rewritten as 612 yards36, or 17 yards.

Choice A is incorrect. This is the number of yards that are equivalent to 2.124 inches.

Choice C is incorrect. This is the number of yards that are equivalent to 20,736 inches.

Choice D is incorrect. This is the number of yards that are equivalent to 793,152 inches.

Question 101 101 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

  • From left to right, the values of the vertical bars in the Class A box plot are as follows:
    • First vertical bar: 0
    • Second vertical bar: 1
    • Third vertical bar: 2
    • Fourth vertical bar: 4
    • Fifth vertical bar: 5
  • From left to right, the values of the vertical bars in the Class B box plot are as follows:
    • First vertical bar: 1
    • Second vertical bar: 4
    • Third vertical bar: 7
    • Fourth vertical bar: 9
    • Fifth vertical bar: 10

 

The two box plots show the distribution of number of books read over the summer by the students in two different English classes. What is the positive difference between the ranges of number of books read over the summer for the two classes?

Show Answer Correct Answer: 4

The correct answer is 4 . It's given that the two boxplots show the distribution of number of books read over the summer by the students in two different English classes. In a boxplot, the first vertical line represents the minimum value of the data set and the last vertical line represents the maximum value of the data set. The range of a data set is the difference between its maximum value and its minimum value. In class A, the maximum number of books read is 5 and the minimum number of books read is 0 . The difference between those values is 5-0, or 5 . Therefore, the range of the number of books read in class A is 5 . In class B, the maximum number of books read is 10 and the minimum number of books read is 1 . The difference between those values is 10-1, or 9 . Therefore, the range of the number of books read in class B is 9 . To find the positive difference between the ranges of the number of books read for the two classes, the smaller range must be subtracted from the larger range. Therefore, the positive difference between the ranges of number of books read over the summer for the two classes is 9-5, or 4 .

Question 102 102 of 368 selected Two-Variable Data: Models And Scatterplots E
The figure presents a graph of 5 line segments titled “Theresa’s Running Speed and Time.” The horizontal axis is labeled “Time,” in minutes, and the numbers zero through 30, in increments of 5, are indicated. The vertical axis is labeled “Speed,” in miles per hour, and the numbers zero through 8 are indicated. 

The first line segment begins at the point with coordinates zero minutes, zero miles per hour, and moves steeply upward and to the right to the point with coordinates 5 minutes, 7 miles per hour. The second line segment begins where the first line segment ends and moves horizontally and to the right to the point with coordinates 10 minutes, 7 miles per hour. The third line segment begins where the second line segment ends and moves gradually downward and to the right to the point with coordinates 20 minutes, 5 miles per hour. The fourth line segment begins where the third line segment ends and moves sharply upward and to the right to the point with coordinates 25 minutes, 8 miles per hour. The fifth line segment begins where the fourth line segment ends and moves steeply downward and to the right to the horizontal axis, ending at the point with coordinates 30 minutes, zero miles per hour.

Theresa ran on a treadmill for thirty minutes, and her time and speed are shown on the graph above. According to the graph, which of the following statements is NOT true concerning Theresa’s run?

  1. Theresa ran at a constant speed for five minutes.

  2. Theresa’s speed was increasing for a longer period of time than it was decreasing.

  3. Theresa’s speed decreased at a constant rate during the last five minutes.

  4. Theresa’s speed reached its maximum during the last ten minutes.

Show Answer Correct Answer: B

Choice B is correct. Theresa’s speed was increasing from 0 to 5 minutes and from 20 to 25 minutes, which is a total of 10 minutes. Theresa’s speed was decreasing from 10 minutes to 20 minutes and from 25 to 30 minutes, which is a total of 15 minutes. Therefore, Theresa’s speed was NOT increasing for a longer period of time than it was decreasing.

Choice A is incorrect. Theresa ran at a constant speed for the 5-minute period from 5 to 10 minutes. Choice C is incorrect. Theresa’s speed decreased at a constant rate during the last 5 minutes, which can be seen since the graph is linear during that time. Choice D is incorrect. Theresa’s speed reached its maximum at 25 minutes, which is within the last 10 minutes.

Question 103 103 of 368 selected Inference From Sample Statistics And Margin Of Error M

A sample consisting of 720 adults who own televisions was selected at random for a study. Based on the sample, it is estimated that 32 % of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41 %. Which of the following is the most plausible conclusion about all adults who own televisions?

  1. More than 35.41 % of all adults who own televisions use their televisions to watch nature shows.

  2. Between 28.59 % and 35.41 % of all adults who own televisions use their televisions to watch nature shows. 

  3. Since the sample included adults who own televisions and not just those who use their televisions to watch nature shows, no conclusion can be made.

  4. Since the sample did not include all the people who watch nature shows, no conclusion can be made.

Show Answer Correct Answer: B

Choice B is correct. It's given that based on a sample selected at random, it's estimated that 32% of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41%. Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true percentage of adults who own televisions who use their televisions to watch nature shows. This means it's plausible that between 32%-3.41%, or 28.59%, and 32%+3.41%, or 35.41%, of all adults who own televisions use their televisions to watch nature shows. Therefore, of the given choices, the most plausible conclusion is that between 28.59% and 35.41% of all adults who own televisions use their televisions to watch nature shows.

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect. To make a plausible conclusion about all adults who own televisions, the sample must be selected at random from all adults who own televisions, not just those who use their televisions to watch nature shows.

Choice D is incorrect. Since the sample was selected at random from all adults who own televisions, a plausible conclusion can be made about all adults who own televisions.

Question 104 104 of 368 selected Percentages M

Last year, Cedric had 35 plants in his garden. This year, the number of plants in Cedric’s garden is 60 % greater than the number of plants in his garden last year. How many plants does Cedric have in his garden this year?

Show Answer Correct Answer: 56

The correct answer is 56 . It’s given that Cedric had 35 plants in his garden last year and that the number of plants in Cedric's garden this year is 60% greater than the number of plants in his garden last year. It follows that the number of plants in Cedric’s garden this year is 35 plus 60% of 35 , which is equal to 35+35(60100), or 35+35(0.6). This expression is equivalent to 35+21, or 56 . Therefore, Cedric has 56 plants in his garden this year.

Question 105 105 of 368 selected Two-Variable Data: Models And Scatterplots M

The scatterplot shows the relationship between two variables, x and y . A line of best fit for the data is also shown.

  • The scatterplot has 11 data points.
  • The data points are in a linear pattern trending down from left to right.
  • A line of best fit is shown:
    • The line of best fit slants down from left to right.
    • 6 points are above the line of best fit.
    • 5 points are below the line of best fit.
    • The line of best fit goes through the following approximate coordinates:
      • (28 comma 6)
      • (33 comma 1.5)

At x = 25.5 , which of the following is closest to the y-value predicted by the line of best fit?

  1. 6.2

  2. 7.3

  3. 8.2

  4. 9.1

Show Answer Correct Answer: C

Choice C is correct. On the line of best fit, an x-value of 25.5 corresponds to a y-value between 8 and 8.5 . Therefore, at x = 25.5 , 8.2 is closest to the y-value predicted by the line of best fit.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.

Question 106 106 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M
International Tourist Arrivals, in millions
Country20122013
France83.084.7
United States66.769.8
Spain57.560.7
China57.755.7
Italy46.447.7
Turkey35.737.8
Germany30.431.5
United Kingdom26.332.2
Russia24.728.4

The table above shows the number of international tourist arrivals, rounded to the nearest tenth of a million, to the top nine tourist destinations in both 2012 and 2013. Based on the information given in the table, how much greater, in millions, was the median number of international tourist arrivals to the top nine tourist destinations in 2013 than the median number in 2012, to the nearest tenth of a million?

 
Show Answer

The correct answer is 1.3. The median number of tourists is found by ordering the number of tourists from least to greatest and determining the middle value from this list. When the number of tourists in 2012 is ordered from least to greatest, the middle value, or the fifth number, is 46.4 million. When the number of tourists in 2013 is ordered from least to greatest, the middle value, or the fifth number, is 47.7 million. The difference between these two medians is 47 point 7 million minus 46 point 4 million, equals 1 point 3 million. Note that 1.3 and 13/10 are examples of ways to enter a correct answer.

Question 107 107 of 368 selected Probability And Conditional Probability E

Of the 8 planets in our solar system, 4 are considered rocky. If a student randomly selects 1 of those 8 planets as a topic for a report, what is the probability that the selected planet will be rocky?

  1. one eighth

  2. one fourth

  3. one half

  4. 2

Show Answer Correct Answer: C

Choice C is correct. If one of these planets is selected at random, the probability that the selected planet will be rocky is calculated by dividing the number of planets that are considered rocky by the total number of planets. It’s given that 4 of the 8 total planets are considered rocky. Therefore, the probability that the selected planet will be rocky is four eighths, which is equivalent to one half.

Choices A and B are incorrect. These represent the probability if 1 of the 8 planets was considered rocky (choice A) and if 2 of the 8 planets were considered rocky (choice B). Choice D is incorrect and may result from dividing the total number of planets by the number of planets that are considered rocky.

 

Question 108 108 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

The dot plots represent the distributions of values in data sets A and B.

  • For the dot plot titled Data Set A:
    • The number line ranges from 10 to 16 in increments of 1.
    • The data for the dot plot are as follows:
      • 10: 1 dot
      • 11: 4 dots
      • 12: 2 dots
      • 13: 3 dots
      • 14: 2 dots
      • 15: 4 dots
      • 16: 1 dot
  • For the dot plot titled Data Set B:
    • The number line ranges from 10 to 16 in increments of 1.
    • The data for the dot plot are as follows:
      • 10: 2 dots
      • 11: 4 dots
      • 12: 2 dots
      • 13: 1 dot
      • 14: 2 dots
      • 15: 4 dots
      • 16: 2 dots

Which of the following statements must be true?

  1. The median of data set A is equal to the median of data set B.
  2. The standard deviation of data set A is equal to the standard deviation of data set B.
  1. I only

  2. II only

  3. I and II

  4. Neither I nor II

Show Answer Correct Answer: A

Choice A is correct. The median of a data set with an odd number of values that are in ascending or descending order is the middle value of the data set. Since the distribution of the values of both data set A and data set B form symmetric dot plots, and each data set has an odd number of values, it follows that the median is given by the middle value in each of the dot plots. Thus, the median of data set A is 13 , and the median of data set B is 13 . Therefore, statement I is true. Data set A and data set B have the same frequency for each of the values 11 , 12 , 14 , and 15 . Data set A has a frequency of 1 for values 10 and 16 , whereas data set B has a frequency of 2 for values 10 and 16 . Standard deviation is a measure of the spread of a data set; it is larger when there are more values further from the mean, and smaller when there are more values closer to the mean. Since both distributions are symmetric with an odd number of values, the mean of each data set is equal to its median. Thus, each data set has a mean of 13 . Since more of the values in data set A are closer to 13 than data set B, it follows that data set A has a smaller standard deviation than data set B. Thus, statement II is false. Therefore, only statement I must be true.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 109 109 of 368 selected Two-Variable Data: Models And Scatterplots M

An inspector begins a day of work with a large sample of shirts that need to be checked for defects. The inspector works at a constant rate throughout the morning. What type of model is best to model the number of shirts remaining to be checked for defects at any given time throughout the morning?

  1. A linear model with a positive slope

  2. A linear model with a negative slope

  3. An exponential growth model

  4. An exponential decay model

Show Answer Correct Answer: B

Choice B is correct. Since the work is done at a constant rate, a linear model best models the situation. The number of shirts remaining is dependent on the length of time the inspector has worked; therefore, if the relationship were graphed, time would be the variable of the horizontal axis and the number of remaining shirts would be the variable of the vertical axis. Since the number of shirts decreases as the time worked increases, it follows that the slope of this graph is negative.

Choice A is incorrect and may result from incorrectly reasoning about the slope. Choices C and D are incorrect and may result from not identifying the constant rate of work as a characteristic of a linear model.

Question 110 110 of 368 selected Probability And Conditional Probability M

At a movie theater, there are a total of 350 customers. Each customer is located in either theater A, theater B, or theater C. If one of these customers is selected at random, the probability of selecting a customer who is located in theater A is 0.48 , and the probability of selecting a customer who is located in theater B is 0.24 . How many customers are located in theater C?

  1. 28

  2. 40

  3. 84

  4. 98

Show Answer Correct Answer: D

Choice D is correct. It’s given that at a movie theater, there are a total of 350 customers and that each customer is located in either theater A, theater B, or theater C. If the probability of selecting a customer in theater A is 0.48 , then (0.48)(350), or 168 , customers are located in theater A. If the probability of selecting a customer in theater B is 0.24 , then (0.24)(350), or 84 , customers are located in theater B. It follows that there are 168+84, or 252 , customers in theater A and theater B. Therefore, there are 350-252, or 98 , customers in theater C.

Choice A is incorrect. This is the percent, not the number, of the customers that are located in theater C.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the number of customers that are located in theater B, not theater C.

Question 111 111 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

The speed of a vehicle is increasing at a rate of 7.3 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth? (Use 1 mile=1,609 meters.)

  1. 0.3

  2. 16.3

  3. 195.8

  4. 220.4

Show Answer Correct Answer: B

Choice B is correct. It's given that the speed of a vehicle is increasing at a rate of 7.3 meters per second squared. It's given to use 1 mile=1,609 meters. There are 60 seconds in 1 minute; therefore, 602 or 3,600 seconds squared is equal to 1 minute squared. It follows that the rate of 7.3 meters per second squared is equivalent to (7.3 meters1 second squared)(1 mile1,609 meters)(3,600 seconds squared1 minute squared), or approximately 16.33 miles per minute squared. The rate, in miles per minute squared, rounded to the nearest tenth is 16.3 .

Choice A is incorrect and may result from conceptual or calculation errors. 

Choice C is incorrect and may result from conceptual or calculation errors. 

Choice D is incorrect and may result from conceptual or calculation errors.

Question 112 112 of 368 selected Probability And Conditional Probability E
  Live east of the river Live west of the river Total
Less than 40 years old 17 11 28
At least 40 years old 18 89 107
Total 35 100 135

The table summarizes members of a local organization by age and whether they live east or west of the river. If a member of the organization is selected at random, what is the probability that the selected member is at least 40 years old? 

  1. 28135

  2. 35135

  3. 100135

  4. 107135

Show Answer Correct Answer: D

Choice D is correct. If a member of the organization is selected at random, the probability that the selected member is at least 40 years old is equal to the number of members who are at least 40 years old divided by the total number of members. According to the table, there are a total of 135 members of the organization, and 107 of these members are at least 40 years old. Therefore, the probability that the selected member is at least 40 years old is 107 135 .

Choice A is incorrect. This is the probability that the selected member is less than 40 years old.

Choice B is incorrect. This is the probability that the selected member lives east of the river.

Choice C is incorrect. This is the probability that the selected member lives west of the river.

Question 113 113 of 368 selected Percentages E

What is 23% of 100 ?

  1. 23

  2. 46

  3. 77

  4. 123

Show Answer Correct Answer: A

Choice A is correct. 23% of 100 can be calculated by multiplying 23100 by 100 , which yields (23100)100, or 23 .

Choice B is incorrect. This is 46%, not 23%, of 100 .

Choice C is incorrect. This is 23% less than 100 , not 23% of 100 .

Choice D is incorrect. This is 23% greater than 100 , not 23% of 100 .

Question 114 114 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the relationship between two variables, x and y . A line of best fit is also shown.

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown.
    • The line of best fit slants up from left to right.
    • 1 point is touching the line of best fit.
    • 5 points are above the line of best fit.
    • 4 points are below the line of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 3)
      • (3 comma 8)
      • (7 comma 15)

Which of the following equations best represents the line of best fit shown?

  1. y=2.8+1.7x

  2. y=2.8-1.7x

  3. y=-2.8+1.7x

  4. y=-2.8-1.7x

Show Answer Correct Answer: A

Choice A is correct. The line of best fit shown intersects the y-axis at a positive y-value and has a positive slope. The graph of an equation of the form y=a+bx, where a and b are constants, intersects the y-axis at a y-value of a and has a slope of b . Of the given choices, only choice A represents a line that intersects the y-axis at a positive y-value, 2.8 , and has a positive slope, 1.7 .

Choice B is incorrect. This equation represents a line that has a negative slope, not a positive slope.

Choice C is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value.

Choice D is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value, and has a negative slope, not a positive slope.

Question 115 115 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

Rectangle A has length 15 and width w. Rectangle B has length 20 and the same length-to-width ratio as rectangle A. What is the width of rectangle B in terms of ?

  1. four-thirds w

  2. w plus 5

  3. three-fourths w

  4. w minus 5

Show Answer Correct Answer: A

Choice A is correct. It’s given that rectangle A has length 15 and width w. Therefore, the length-to-width ratio of rectangle A is 15 to w. It’s also given that rectangle B has length 20 and the same length-to-width ratio as rectangle A. Let x represent the width of rectangle B. The proportion 15 over w, equals, 20 over x can be used to solve for x in terms of w. Multiplying both sides of this equation by x yields the fraction 15 x over w, equals 20, and then multiplying both sides of this equation by w yields 15 x equals 20 w. Dividing both sides of this equation by 15 yields x equals, the fraction 20 w over 15. Simplifying this fraction yields x equals, four thirds w.

Choices B and D are incorrect and may result from interpreting the difference in the lengths of rectangle A and rectangle B as equivalent to the difference in the widths of rectangle A and rectangle B. Choice C is incorrect and may result from using a length-to-width ratio of w to 15, instead of 15 to w.

 

Question 116 116 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H
Weight (pounds) Frequency
13 12
14 8
15 5
16 7
17 9
18 10
19 13
20 7

The frequency table summarizes a data set of the weights, rounded to the nearest pound, of 71 tortoises. A weight of 39 pounds is added to the original data set, creating a new data set of the weights, rounded to the nearest pound, of 72 tortoises. Which statement best compares the mean and median of the new data set to the mean and median of the original data set?

  1. The mean of the new data set is greater than the mean of the original data set, and the median of the new data set is greater than the median of the original data set.

  2. The mean of the new data set is greater than the mean of the original data set, and the medians of the two data sets are equal.

  3. The mean of the new data set is less than the mean of the original data set, and the median of the new data set is less than the median of the original data set.

  4. The mean of the new data set is less than the mean of the original data set, and the medians of the two data sets are equal.

Show Answer Correct Answer: B

Choice B is correct. The mean of a data set is the sum of the values in the data set divided by the number of values in the data set. The new data set consists of the weights of the 71 tortoises in the original data set and one additional weight, 39 . Since the additional weight, 39 , is greater than any of the values in the original data set, the mean of the new data set is greater than the mean of the original data set. If a data set contains an odd number of data values, the median is represented by the middle data value in the list when the data values are listed in ascending or descending order. Since the original data set consists of the weights of 71 tortoises and is in ascending order, the median of the original data set is represented by the middle value, or the 36 th value. Based on the frequencies shown in the table, the 36 th value in this data set is 17 . If a data set contains an even number of data values, the median is between the two middle data values when the values are listed in ascending or descending order. Since the new data set consists of the weights of 72 tortoises, the median of the new data set is between the 36 th and 37 th data values when the values are arranged in ascending order. To keep the data in ascending order, the additional value of 39 would be placed at the bottom of the frequency table with a frequency of 1 . Therefore, based on the frequencies in the table, the 36 th and 37 th values in the new data set are both 17 . It follows that the median of the new data set is 17 , which is the same as the median of the original data set. Therefore, the mean of the new data set is greater than the mean of the original data set, and the medians of the two data sets are equal.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 117 117 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

Shaquan has 7 red cards and 28 blue cards. What is the ratio of red cards to blue cards that Shaquan has?

  1. 1 to 4

  2. 4 to 1

  3. 1 to 7

  4. 7 to 1

Show Answer Correct Answer: A

Choice A is correct. It’s given that Shaquan has 7 red cards and 28 blue cards. Therefore, the ratio of red cards to blue cards that Shaquan has is 7 to 28. This ratio can be reduced by dividing both parts of the ratio by 7, which yields the ratio 1 to 4.

Choice B is incorrect. This is the ratio of blue cards to red cards that Shaquan has. Choice C is incorrect and may result from a calculation error when reducing the ratio. Choice D is incorrect. This may result from finding the ratio of blue cards to red cards, or 28 to 7, and then making a calculation error when reducing the ratio.

Question 118 118 of 368 selected Two-Variable Data: Models And Scatterplots M
The figure presents a scatterplot titled “Income and Percent of Total Expenses Spent on Programs for Ten Charities in 2011.” The horizontal axis is labeled “Total income,” in millions of dollars, and the numbers zero through 7,000, in increments of 1,000, are indicated. The vertical axis is labeled “Percent of total expenses spent on programs” and the numbers 70 through 95, in increments of 5, are indicated. 

The 10 data points on the graph are presented in the following list. All data are approximate.

1,300 million dollars; 74 percent. 
1,500 million dollars; 82 percent.
1,550 million dollars; 84 percent.
1,550 million dollars; 85 percent.
3,300 million dollars; 84 percent.
3,400 million dollars; 92 percent.
4,200 million dollars; 91 percent.
4,500 million dollars; 89 percent.
4,500 million dollars; 80 percent.
6,000 million dollars; 87 percent.

The line of best fit is also shown and passes through the following coordinates on the graph. All values are approximate. 

1,200 million dollars; 81 percent. 
3,500 million dollars; 85 percent.
5,000 million dollars; 88 percent.

The scatterplot above shows data for ten charities along with the line of best fit. For the charity with the greatest percent of total expenses spent on programs, which of the following is closest to the difference of the actual percent and the percent predicted by the line of best fit?

  1. 10 percent

  2. 7 percent

  3. 4 percent

  4. 1 percent

Show Answer Correct Answer: B

Choice B is correct. The charity with the greatest percent of total expenses spent on programs is represented by the highest point on the scatterplot; this is the point that has a vertical coordinate slightly less than halfway between 90 and 95 and a horizontal coordinate slightly less than halfway between 3,000 and 4,000. Thus, the charity represented by this point has a total income of about $3,400 million and spends about 92% of its total expenses on programs. The percent predicted by the line of best fit is the vertical coordinate of the point on the line of best fit with horizontal coordinate $3,400 million; this vertical coordinate is very slightly more than 85. Thus, the line of best fit predicts that the charity with the greatest percent of total expenses spent on programs will spend slightly more than 85% on programs. Therefore, the difference between the actual percent (92%) and the prediction (slightly more than 85%) is slightly less than 7%.

Choice A is incorrect. There is no charity represented in the scatterplot for which the difference between the actual percent of total expenses spent on programs and the percent predicted by the line of best fit is as much as 10%. Choices C and D are incorrect. These choices may result from misidentifying in the scatterplot the point that represents the charity with the greatest percent of total expenses spent on programs.

 

Question 119 119 of 368 selected Percentages H

The number a is 190% greater than the number b . The number b is 80% less than 24. What is the value of a ?

  1. 9.12

  2. 13.92

  3. 26.40

  4. 36.48

Show Answer Correct Answer: B

Choice B is correct. It's given that the number b is 80% less than 24 . It follows that b is equal to 24 minus 80% of 24 , which can be written as b=24-(80100)24. This is equivalent to b=24-0.8(24), or b = 4.8 . It's also given that the number a is 190% greater than the number b . It follows that a is equal to b plus 190% of b . Since b = 4.8 , this can be written as a=4.8+(190100)4.8. This is equivalent to a=4.8+1.9(4.8), or a = 13.92 .

Choice A is incorrect. This would be the value of a if a were 190% of b , not 190% greater than b .

Choice C is incorrect. This is (190-80)% of 24 .

Choice D is incorrect. This would be the value of a if b were 80% of 24 , not 80% less than 24 , and a were 190% of b , not 190% greater than b .

Question 120 120 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

An object has a mass of 168 grams and a volume of 24 cubic centimeters. What is the density, in grams per cubic centimeter, of the object?

  1. 7

  2. 144

  3. 192

  4. 4,032

Show Answer Correct Answer: A

Choice A is correct. It's given that the object has a mass of 168 grams and a volume of 24 cubic centimeters. Dividing the mass, in grams, of the object by the volume, in cubic centimeters, of the object gives the density, in grams per cubic centimeter, of the object. It follows that the density of the object is 168 grams24 cubic centimeters, which is equivalent to 16824 grams per cubic centimeter, or 7 grams per cubic centimeter.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 121 121 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A giant armadillo has a mass of 39 kilograms. What is the giant armadillo's mass in grams(1 kilogram=1,000 grams)

Show Answer Correct Answer: 39000

The correct answer is 39,000 . It’s given that the giant armadillo has a mass of 39 kilograms. Since 1 kilogram is equal to 1,000 grams, 39 kilograms is equal to 39 kilograms (1,000 grams1 kilogram), or 39,000 grams. Therefore, the giant armadillo’s mass, in grams, is 39,000 .

Question 122 122 of 368 selected Inference From Sample Statistics And Margin Of Error M

A company fills boxes with approximately 23 pounds of oranges. To test the accuracy of the filling process, 344 boxes of oranges were selected at random and weighed. Based on the sample, it is estimated that the average weight of all boxes of oranges filled by the company in an 8 -hour period is 23.1 pounds, with an associated margin of error of 0.19 pounds. Which of the following is the best interpretation of this estimate?

  1. Plausible values for the average weight of all boxes of oranges filled by the company are between 22.91 pounds and 23.29 pounds.

  2. Plausible values for the average weight of all boxes of oranges filled by the company are less than 22.91 pounds or greater than 23.29 pounds.

  3. The average weight of all boxes of oranges filled by the company is less than 23.01 pounds.

  4. The average weight of all boxes of oranges filled by the company is greater than 23.01 pounds.

Show Answer Correct Answer: A

Choice A is correct. It's given that the estimate for the average weight of all boxes of oranges filled by the company in an 8 -hour period is 23.1 pounds, with an associated margin of error of 0.19 pounds. It follows that plausible values for this average weight are between 23.1-0.19 pounds and 23.1+0.19 pounds. Therefore, plausible values for the average weight of all boxes of oranges filled by the company are between 22.91 pounds and 23.29 pounds.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 123 123 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

The table shown summarizes the number of employees at each of the 17 restaurants in a town.

Number of employees Number of restaurants
2 to 7 2
8 to 13 4
14 to 19 2
20 to 25 7
26 to 31 2

Which of the following could be the median number of employees for the restaurants in this town?

  1. 2

  2. 9

  3. 15

  4. 21

Show Answer Correct Answer: D

Choice D is correct. If a data set contains an odd number of data values, the median is represented by the middle data value in the list when the data values are listed in ascending or descending order. Since the numbers of employees are given as ranges of values rather than specific values, it's only possible to determine the range in which the median falls, rather than the exact median. Since there are 17 restaurants included in the data set and the numbers of employees are listed in ascending order, it follows that the median number of employees will be represented by the ninth restaurant in the list. Since the first 2 restaurants each have 2 to 7 employees, numbers of employees in the 2 to 7 range would be represented by the first and second restaurants in the list. The next 4 restaurants each have 8 to 13 employees. Therefore, numbers of employees in the 8 to 13 range will be represented by the third through sixth restaurants in the list. The next 2 restaurants each have 14 to 19 employees. Therefore, numbers of employees in the 14 to 19 range will be represented by the seventh and eighth restaurants in the list. Since the next 7 restaurants each have 20 to 25 employees, numbers of employees in the 20 to 25 range will be represented by the ninth through fifteenth restaurants in the list. This means that the ninth restaurant in the list, which has the median number of employees for the restaurants in this town, has a number of employees in the 20 to 25 range. Of the given choices, the only number of employees in the 20 to 25 range is 21 .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the position of the median in the list, not the value of the median.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 124 124 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

  • Data Set A:
    • The horizontal axis is labeled Integer. It ranges from 10 to 60 and is divided into 5 equal intervals.
    • The vertical axis is labeled Frequency. It ranges from 0 to 12 in increments of 1, with values marked every 2 grid lines.
    • The histogram has a skewed right shape.
    • The histogram has 4 bins.
    • The Frequency data for the 4 bins are as follows:
      • 20 to 30: 3
      • 30 to 40: 4
      • 40 to 50: 7
      • 50 to 60: 9
  • Data Set B:
    • The horizontal axis is labeled Integer. It ranges from 10 to 60 and is divided into 5 equal intervals.
    • The vertical axis is labeled Frequency. It ranges from 0 to 12 in increments of 1, with values marked every 2 grid lines.
    • The histogram has a skewed right shape.
    • The histogram has 4 bins.
    • The Frequency data for the 4 bins are as follows:
      • 10 to 20: 3
      • 20 to 30: 4
      • 30 to 40: 7
      • 40 to 50: 9

Two data sets of 23 integers each are summarized in the histograms shown. For each of the histograms, the first interval represents the frequency of integers greater than or equal to 10 , but less than 20 . The second interval represents the frequency of integers greater than or equal to 20 , but less than 30 , and so on. What is the smallest possible difference between the mean of data set A and the mean of data set B?

  1. 0

  2. 1

  3. 10

  4. 23

Show Answer Correct Answer: B

Choice B is correct. The histograms shown have the same shape, but data set A contains values between 20 and 60 and data set B contains values between 10 and 50 . Thus, the mean of data set A is greater than the mean of data set B. Therefore, the smallest possible difference between the mean of data set A and the mean of data set B is the difference between the smallest possible mean of data set A and the greatest possible mean of data set B. In data set A, since there are 3 integers in the interval greater than or equal to 20 but less than 30 , 4 integers greater than or equal to 30 but less than 40 , 7 integers greater than or equal to 40 but less than 50 , and 9 integers greater than or equal to 50 but less than 60 , the smallest possible mean for data set A is (3·20)+(4·30)+(7·40)+(9·50)23. In data set B, since there are 3 integers greater than or equal to 10 but less than 20 , 4 integers greater than or equal to 20 but less than 30 , 7 integers greater than or equal to 30 but less than 40 , and 9 integers greater than or equal to 40 but less than 50 , the largest possible mean for data set B is (3·19)+(4·29)+(7·39)+(9·49)23. Therefore, the smallest possible difference between the mean of data set A and the mean of data set B is (3·20)+(4·30)+(7·40)+(9·50)23-(3·19)+(4·29)+(7·39)+(9·49)23, which is equivalent to (3·20)-(3·19)+(4·30)-(4·29)+(7·40)-(7·39)+(9·50)-(9·49)23. This expression can be rewritten as 3(20-19)+4(30-29)+7(40-39)+9(50-49)23, or 2323, which is equal to 1 . Therefore, the smallest possible difference between the mean of data set A and the mean of data set B is 1 .

Choice A is incorrect. This is the smallest possible difference between the ranges, not the means, of the data sets.

Choice C is incorrect. This is the difference between the greatest possible mean, not the smallest possible mean, of data set A and the greatest possible mean of data set B.

Choice D is incorrect. This is the smallest possible difference between the sum of the values in data set A and the sum of the values in data set B, not the smallest possible difference between the means.

Question 125 125 of 368 selected Inference From Sample Statistics And Margin Of Error E

A random sample of 50 people from a town with a population of 14,878 were asked to name their favorite flavor of ice cream. If 7 people in the sample named chocolate as their favorite ice‑cream flavor, about how many people in the town would be expected to name chocolate?

  1. 350
  2. 2,100
  3. 7,500
  4. 10,500
Show Answer Correct Answer: B

Choice B is correct. Let x be the number of people in the entire town that would be expected to name chocolate. Since the sample of 50 people was selected at random, it is reasonable to expect that the proportion of people who named chocolate as their favorite ice-cream flavor would be the same for both the sample and the town population. Symbolically, this can be expressed as the fraction 7 over 50, end fraction, equals, the fraction x over 14,878. Using cross multiplication, 7 times 14,878 equals, x times 50; solving for x yields 2,083. The choice closest to the value of 2,083 is choice B, 2,100.

Choices A, C, and D are incorrect and may be the result of errors when setting up the proportion, solving for the unknown, or incorrectly comparing the choices to the number of people expected to name chocolate, 2,083.

Question 126 126 of 368 selected Probability And Conditional Probability M

Each vertex of a 14 -sided polygon is labeled with one of the 14 letters A through N , with a different letter at each vertex. If one vertex is selected at random, what is the probability that the letter D will be at the selected vertex? (Express your answer as a decimal or fraction, not as a percent.)

Show Answer Correct Answer: .0714, 1/14

The correct answer is 1 14 . If one vertex of the polygon is selected at random, the probability that the letter D will be at the selected vertex is equal to the number of vertices labeled with the letter D divided by the total number of vertices. It's given that each vertex is labeled with one of the 14 letters A through N , with a different letter at each vertex. It follows that there is 1 vertex labeled with the letter D . It's also given that the polygon is 14 -sided. It follows that there are a total of 14 vertices. Thus, the probability that the letter D will be at the selected vertex is 1 14 . Note that 1/14, .0714, and 0.071 are examples of ways to enter a correct answer.

Question 127 127 of 368 selected Percentages M

Which expression represents the result of increasing a positive quantity w by 43%?

  1. 1.43w

  2. 0.57w

  3. 43 w

  4. 0.43w

Show Answer Correct Answer: A

Choice A is correct. The result of increasing a positive quantity w by x% can be represented by the expression (1+x100)w. Therefore, the result of increasing a positive quantity w by 43% can be found by substituting 43 for x in the expression (1+x100)w, which gives (1+43100)w, or 1.43w. Thus, the expression 1.43w represents the result of increasing a positive quantity w by 43%.

Choice B is incorrect. This is the result of decreasing a positive quantity w by 43%.

Choice C is incorrect. This is the result of increasing a positive quantity w by 4,200%.

Choice D is incorrect. This is the result of decreasing a positive quantity w by 57%.

Question 128 128 of 368 selected Probability And Conditional Probability E
Texting behaviorTalks on cell phone dailyDoes not talk on cell phone dailyTotal
Light110146256
Medium139164303
Heavy16674240
Total415384799
 

In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. If one of the 799 teens surveyed is selected at random, what is the probability that the teen talks on a cell phone daily?

  1. 1 over 799

  2. 415 over 799

  3. 384 over 415

  4. 384 over 799

Show Answer Correct Answer: B

Choice B is correct. If one of the teens surveyed is selected at random, the probability that the teen talks on a cell phone daily is equal to the quotient of the total number of teens who reported that they talk on a cell phone daily, 415, and the total number of teens surveyed, 799. Therefore, this probability is equal to 415 over 799.

Choice A is incorrect. This fraction represents the probability of selecting at random any one of the 799 teens surveyed. Choice C is incorrect and may result from conceptual errors. Choice D is incorrect. This fraction represents the probability of selecting at random one of the 799 teens surveyed who doesn’t talk on a cell phone daily. 

Question 129 129 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

How many yards are equivalent to 77 rods? (5.5 yards=1 rod)

Show Answer Correct Answer: 423.5, 847/2

The correct answer is 423.5. It's given that 5.5 yards=1 rod. Therefore, 77 rods is equivalent to (77 rods)(5.5 yards1 rod), or 423.5 yards. Note that 423.5 and 847/2 are examples of ways to enter a correct answer.

Question 130 130 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

Jeremy deposited x dollars in his investment account on January 1, 2001. The amount of money in the account doubled each year until Jeremy had 480 dollars in his investment account on January 1, 2005. What is the value of ?

Show Answer

The correct answer is 30. The situation can be represented by the equation x times, open parenthesis, 2 to the fourth power, close parenthesis, equals 480, where the 2 represents the fact that the amount of money in the account doubled each year and the 4 represents the fact that there are 4 years between January 1, 2001, and January 1, 2005. Simplifying x times, open parenthesis, 2 to the fourth power, close parenthesis, equals 480 gives 16 x equals 480. Therefore, x equals 30.

Question 131 131 of 368 selected Two-Variable Data: Models And Scatterplots M

The scatterplot shows the relationship between two variables, x and y . A line of best fit for the data is also shown.

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • 6 points are above the line of best fit.
    • 4 points are below the line of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 0.1)
      • (5 comma 5.1)

For how many of the 10 data points is the actual y-value greater than the y-value predicted by the line of best fit?

  1. 3

  2. 4

  3. 6

  4. 7

Show Answer Correct Answer: C

Choice C is correct. Any data point that's located above the line of best fit has a y-value that's greater than the y-value predicted by the line of best fit. For the scatterplot shown, 6 of the data points are above the line of best fit. Therefore, 6 of the data points have an actual y-value that's greater than the y-value predicted by the line of best fit.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the number of data points that have an actual y-value that's less than the y-value predicted by the line of best fit.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 132 132 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

2 , 9 , 14 , 23 , 32

What is the mean of the data shown?

  1. 14

  2. 16

  3. 17

  4. 32

Show Answer Correct Answer: B

Choice B is correct. The mean of a set of data values is the sum of all the data values divided by the number of data values in the set. The sum of the data values shown is 2+9+14+23+32, or 80 . Since there are 5 data values in the set, the mean of the data shown is 805, or 16 .

Choice A is incorrect. This is the median, not the mean, of the data shown.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the maximum, not the mean, of the data shown.

Question 133 133 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H
Value Frequency
1 a
2 2a
3 3a
4 2a
5 a

The frequency distribution above summarizes a set of data, where a is a positive integer. How much greater is the mean of the set of data than the median?

  1. 0

  2. 1

  3. 2

  4. 3

Show Answer Correct Answer: A

Choice A is correct. Since the frequencies of values less than the middle value, 3, are the same as the frequencies of the values greater than 3, the set of data has a symmetric distribution. When a set of data has a symmetric distribution, the mean and median values are equal. Therefore, the mean is 0 greater than the median.

Choices B, C, and D are incorrect and may result from misinterpreting the set of data.

 

Question 134 134 of 368 selected Probability And Conditional Probability E

A band with 45 members has 11 members who play saxophone. If one band member is selected at random, what is the probability of selecting a band member who plays saxophone?

  1. 145

  2. 1145

  3. 3445

  4. 4545

Show Answer Correct Answer: B

Choice B is correct. The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes. It’s given that there are 45 band members, which is the total number of possible outcomes. It's also given that there are 11 band members who play saxophone. Therefore, the number of favorable outcomes is 11 . Thus, the probability of selecting a band member who plays saxophone is 1145.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the probability of selecting a band member who does not play saxophone.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 135 135 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

Tanya earns $13.50 per hour at her part-time job. When she works z hours, she earns 13 point 5 0 z dollars. Which of the following expressions gives the amount, in dollars, Tanya will earn if she works 3 z hours?

  1. 3 times, open parenthesis, 13 point 5 0 z, close parenthesis

  2. 3 plus 13 point 5 0 z

  3. 3 z plus 13 point 5 0 z

  4. 13 point 5 0 times, open parenthesis, z plus 3, close parenthesis

Show Answer Correct Answer: A

Choice A is correct. It’s given that when Tanya works z hours, she earns 13 point 5 0 z dollars. Since her hourly rate is constant, if she works 3 times as many hours, or 3 z hours, she will earn 3 times as many dollars, or 3 times, open parenthesis, 13 point 5 0 z, close parenthesis.

Choice B is incorrect. This expression represents adding 3 dollars to the 13 point 5 0 z dollars Tanya will earn. Choice C is incorrect. This expression can be rewritten as 16 point 5 0 z, which implies that Tanya earns $16.50 per hour, not $13.50. Choice D is incorrect. This expression adds 3 to the number of hours Tanya works, rather than multiplying the hours she works by 3.

 

Question 136 136 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

Two different teams consisting of 10 members each ran in a race. Each member’s completion time of the race was recorded. The mean of the completion times for each team was calculated and is shown below.

Team A: 3.41 minutes
Team B: 3.79 minutes

Which of the following MUST be true?

  1. Every member of team A completed the race in less time than any member of team B.
  2. The median time it took the members of team B to complete the race is greater than the median time it took the members of team A to complete the race.
  3. There is at least one member of team B who took more time to complete the race than some member of team A.

  1. III only

  2. I and III only

  3. II and III only

  4. I, II, and III

Show Answer Correct Answer: A

Choice A is correct. Since the average time for the 10 members of team A is 3.41 minutes, the sum of the 10 times for team A is equal to 10 times 3 point 4 1, equals 34 point 1 minutes. Since the average time for the 10 members of team B is 3.79 minutes, the sum of the 10 times for team B is equal to 10 times 3 point 7 9, equals 37 point 9 minutes. Since the sum of the 10 times for team B is greater than the sum of the 10 times for team A, it must be true that at least one of the times for team B must be greater than one of the times for team A. Thus, statement III is true. However, it’s possible that at least some of the times for team A were greater than some of the times for team B. For example, all of team A’s times could be 3.41 minutes, and team B could have 1 time of 3.34 minutes and 9 times of 3.84 minutes. Thus, statement I need not be true. It’s also possible that the median of the times for team B is less than the median of the times for team A. For example, all of team A’s times could be 3.41 minutes, and team B could have 6 times of 3.37 minutes and 4 times of 4.42 minutes; then the median of team B’s times would be 3.37 minutes and the median of team A’s times would be 3.41 minutes. Thus, statement II need not be true.

Choices B, C, and D are incorrect because neither statement I nor statement II must be true.

Question 137 137 of 368 selected Percentages M

The population of City A increased by 7% from 2015 to 2016. If the 2016 population is k times the 2015 population, what is the value of k ?

  1. 0.07

  2. 0.7

  3. 1.07

  4. 1.7

Show Answer Correct Answer: C

Choice C is correct. It's given that the population of City A increased by 7% from 20 15 to 20 16 . Therefore, the population of City A in 20 16 includes 100% of the population of City A in 20 15 plus an additional 7% of the population of City A in 20 15 . This means that the population of City A in 20 16 is 107% of the population in 20 15 . Thus, the population of City A in 20 16 is 107 100 , or 1.07 , times the 20 15 population. Therefore, the value of k is 1.07 .

Choice A is incorrect. This would be the value of k if the population in 20 16 was 7% of the population in 20 15 .

Choice B is incorrect. This would be the value of k if the population in 20 16 was 70% of the population in 20 15 .

Choice D is incorrect. This would be the value of k if the population increased by 70%, not 7%, from 20 15 to 20 16 .

Question 138 138 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

  1. 20

  2. 24

  3. 32

  4. 36

Show Answer Correct Answer: C

Choice C is correct. If the mean score of 8 players is 14.5, then the total of all 8 scores is 14 point 5 times 8, equals 116. If the mean of 7 scores is 12, then the total of all 7 scores is 12 times 7, equals 84. Since the set of 7 scores was made by removing the highest score of the set of 8 scores, then the difference between the total of all 8 scores and the total of all 7 scores is equal to the removed score: 116 minus 84, equals 32.

Choice A is incorrect because if 20 is removed from the group of 8 scores, then the mean score of the remaining 7 players is the fraction with numerator, open parenthesis, 14 point 5 times 8, close parenthesis, minus 20, and denominator 7 is approximately 13.71, not 12. Choice B is incorrect because if 24 is removed from the group of 8 scores, then the mean score of the remaining 7 players is the fraction with numerator, open parenthesis, 14 point 5 times 8, close parenthesis, minus 24, and denominator 7 is approximately 13.14, not 12. Choice D is incorrect because if 36 is removed from the group of 8 scores, then the mean score of the remaining 7 players is the fraction with numerator, open parenthesis, 14 point 5 times 8, close parenthesis, minus 36, and denominator 7 or approximately 11.43, not 12.

 

Question 139 139 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

The list gives the mass, in grams, of 5 alpine marmots. 

 4,010 ; 4,010 ; 3,030 ; 4,050 ; 3,050

What is the mean mass, in grams, of these 5 alpine marmots? 

Show Answer Correct Answer: 3630

The correct answer is 3,630 . The mean of a data set is the sum of the values in the data set divided by the number of values in the data set. The sum of the masses, in grams, of these alpine marmots is 4,010+4,010+3,030+4,050+3,050, or 18,150 grams. The number of alpine marmots in the data set is 5 . Therefore, the mean mass, in grams, of these 5 alpine marmots is 18,1505, or 3,630 .

Question 140 140 of 368 selected Inference From Sample Statistics And Margin Of Error M

A company that produces socks wants to estimate the percent of the socks produced in a typical week that are defective. A random sample of 310 socks produced in a certain week were inspected. Based on the sample, it is estimated that 12 % of all socks produced by the company in this week are defective, with an associated margin of error of 3.62 %. Based on the estimate and associated margin of error, which of the following is the most appropriate conclusion about all socks produced by the company during this week?

  1. 3.62 % of the socks are defective.

  2. It is plausible that between 8.38 % and 15.62 % of the socks are defective.

  3. 12 % of the socks are defective.

  4. It is plausible that more than 15.62 % of the socks are defective.

Show Answer Correct Answer: B

Choice B is correct. It’s given that, based on the sample, an estimate of 12% of all socks produced by the company in a certain week are defective, with an associated margin of error of 3.62%. This estimate, plus or minus the margin of error, gives an interval of plausible values for the actual percent of all socks produced by the company that week that are defective. Subtracting 3.62% from 12% yields 8.38%. Adding 3.62% to 12% yields 15.62%. Therefore, it is plausible that between 8.38% and 15.62% of all socks produced by the company are defective.

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect. 12% is the estimated percent of defective socks based on the sample. However, since the margin of error for this estimate is known, the most appropriate conclusion is not that the percent of defective socks is exactly 12% but instead that it lies in an interval of plausible percents.

Choice D is incorrect and may result from conceptual errors.

Question 141 141 of 368 selected Two-Variable Data: Models And Scatterplots H
The figure presents a scatterplot titled “Ice Cream Sales.” The horizontal axis is labeled “Temperature, in degrees Celsius,” and the integers 10 through 26, in increments of 2, are indicated. The vertical axis is labeled “Sales, in dollars,” and the integers 300 through 1,000, in increments of 100, are indicated. There are 12 data points in the scatterplot, and the line of best fit is drawn. The line of best fit begins slightly above the horizontal axis, and slightly to the right of the vertical axis, and slants upward and to the right. It passes through the point 12 comma 480 and the point 24 comma 880.

The scatterplot above shows a company’s ice cream sales d, in dollars, and the high temperature t, in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?

  1. d equals, 0 point 0 3 t plus 402

  2. d equals, 10 t plus 402

  3. d equals, 33 t plus 300

  4. d equals, 33 t plus 84

Show Answer Correct Answer: D

Choice D is correct. On the line of best fit, d increases from approximately 480 to 880 between t equals 12 and t equals 24. The slope of the line of best fit is the difference in d-values divided by the difference in t-values, which gives the fraction with numerator 880 minus 480, and denominator 24 minus 12, end fraction, equals, the fraction 400 over 12, or approximately 33. Writing the equation of the line of best fit in slope-intercept form gives d equals, 33 t plus b, where b is the y-coordinate of the y-intercept. This equation is satisfied by all points on the line, so d equals 480 when t equals 12. Thus, 480 equals, 33 times 12, plus b, which is equivalent to 480 equals, 396 plus b. Subtracting 396 from both sides of this equation gives b equals 84. Therefore, an equation for the line of best fit could be d equals, 33 t plus 84.

Choice A is incorrect and may result from an error in calculating the slope and misidentifying the y-coordinate of the y-intercept of the graph as the value of d at rather than the value of d at t equals 0. Choice B is incorrect and may result from using the smallest value of t on the graph as the slope and misidentifying the y-coordinate of the y-intercept of the graph as the value of d at t equals 10 rather than the value of d at t equals 0. Choice C is incorrect and may result from misidentifying the y-coordinate of the y-intercept as the smallest value of d on the graph.

 

Question 142 142 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A cherry pitting machine pits 12 pounds of cherries in 3 minutes. At this rate, how many minutes does it take the machine to pit 96 pounds of cherries?

  1. 8

  2. 15

  3. 24

  4. 36

Show Answer Correct Answer: C

Choice C is correct. It's given that the cherry pitting machine pits 12 pounds of cherries in 3 minutes. This rate can be written as 12 pounds of cherries3 minutes. If the number of minutes it takes the machine to pit 96 pounds of cherries is represented by x , the value of x can be calculated by solving the equation 12 pounds of cherries3 minutes=96 pounds of cherriesx minutes, which can be rewritten as 123=96x, or 4=96x. Multiplying each side of this equation by x yields 4x=96. Dividing each side of this equation by 4 yields x=24. Therefore, it takes the machine 24 minutes to pit 96 pounds of cherries.

Choice A is incorrect. This is the number of minutes it takes the machine to pit 32 , not 96 , pounds of cherries. 

Choice B is incorrect. This is the number of minutes it takes the machine to pit 60 , not 96 , pounds of cherries. 

Choice D is incorrect. This is the number of minutes it takes the machine to pit 144 , not 96 , pounds of cherries. 

Question 143 143 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A kangaroo has a mass of 28 kilograms. What is the kangaroo's mass, in grams(1 kilogram=1,000 grams)

  1. 28,000

  2. 1,028

  3. 972

  4. 784

Show Answer Correct Answer: A

Choice A is correct. It's given that a kangaroo has a mass of 28 kilograms and that 1 kilogram is equal to 1,000 grams. Therefore, the kangaroo's mass, in grams, is 28 kilograms(1,000 grams1 kilogram), which is equivalent to 28,000 grams.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 144 144 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

The figure presents a cylindrical shape with a circular base and a larger circular top. The diameter of the circular base is labeled “k over 2,” the diameter of the circular top is labeled “k,” and the height is labeled “k.” The volume of the figure is equal to the fraction with numerator 7 pi k cubed, and denominator 48

The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill the glass with 1 gallon of water? 1 gallon equals 128 fluid ounces

  1. 16

  2.   8

  3.   4

  4.   3

Show Answer Correct Answer: B

Choice B is correct. It is given that the volume of the glass is approximately 16 fluid ounces. If Jenny has 1 gallon of water, which is 128 fluid ounces, she could fill the glass 128 over 16, which equals 8 times.

Choice A is incorrect because Jenny would need 16 times 16 fluid ounces = 256 fluid ounces, or 2 gallons, of water to fill the glass 16 times. Choice C is incorrect because Jenny would need only 4 times 16 fluid ounces = 64 fluid ounces of water to fill the glass 4 times. Choice D is incorrect because Jenny would need only 3 times 16 fluid ounces = 48 fluid ounces to fill the glass 3 times.

Question 145 145 of 368 selected Percentages E

What is 10% of 470 ?

  1. 37

  2. 47

  3. 423

  4. 460

Show Answer Correct Answer: B

Choice B is correct. 10% of a quantity means 10100 times the quantity. Therefore, 10% of 470 can be represented as 10100(470), which is equivalent to 0.10(470), or 47 . Therefore, 10% of 470 is 47 .

Choice A is incorrect. This is 10% of 370 , not 10% of 470 .

Choice C is incorrect. This is 90% of 470 , not 10% of 470 .

Choice D is incorrect. This is 470-10, not 10% of 470 .

Question 146 146 of 368 selected Two-Variable Data: Models And Scatterplots E

1009080706050403020100Probability of snow (%)TuesdayWednesdayThursdayFridayDay of the week
  • The line graph:
    • Begins at Tuesday, 60%
    • Rises sharply to Wednesday, 90%
    • Falls sharply to Thursday, 30%
    • Rises sharply to Friday, 70%

The line graph shows the probability of snow, as a percent, at a certain location for each day during a four-day period. According to the line graph, for which day during this four-day period is the probability of snow 30%?

  1. Tuesday

  2. Wednesday

  3. Thursday

  4. Friday

Show Answer Correct Answer: C

Choice C is correct. For the line graph shown, the probability of snow, as a percent, is represented on the vertical axis. According to the line graph, during this four-day period, the probability of snow is 30% for Thursday.

Choice A is incorrect. The probability of snow on Tuesday is 60%.

Choice B is incorrect. The probability of snow on Wednesday is 90%.

Choice D is incorrect. The probability of snow on Friday is 70%.

Question 147 147 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E
Type of store Average number of employees
Warehouse store 365
Department store 213
Supermarket 130

For a certain region, the table shows the average number of store employees in 2016 by type of store. Based on the table, how much greater was the average number of store employees in warehouse stores than in supermarkets?

  1. 83

  2. 152

  3. 235

  4. 495

Show Answer Correct Answer: C

Choice C is correct. The table shows that for a certain region in 2016, the average number of store employees in warehouse stores was 365 and the average number of store employees in supermarkets was 130 . Subtracting 130 from 365 yields 365-130, or 235 . Therefore, the average number of store employees was 235 greater in warehouse stores than in supermarkets.

Choice A is incorrect. For this region in 2016, this is how much greater the average number of store employees was in department stores than in supermarkets.

Choice B is incorrect. For this region in 2016, this is how much greater the average number of store employees was in warehouse stores than in department stores.

Choice D is incorrect. For this region in 2016, this is the sum of the average number of store employees in warehouse stores and in supermarkets.

Question 148 148 of 368 selected Inference From Sample Statistics And Margin Of Error M

A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red beads in the bag, a sample of beads is selected at random. The percent of red beads in the bag was estimated to be 15%, with an associated margin of error of 2%. If r is the actual number of red beads in the bag, which of the following is most plausible?

  1. r is greater than 1,700

  2. 1,300 is less than r, which is less than 1,700

  3. 200 is less than r, which is less than 1,500

  4. r is less than 1,300

Show Answer Correct Answer: B

Choice B is correct. It was estimated that 15% of the beads in the bag are red. Since the bag contains 10,000 beads, it follows that there are an estimated 10,000 times 0 point 1 5, equals 1,500 red beads. It’s given that the margin of error is 2%, or 10,000 times 0 point 0 2, equals 200 beads. If the estimate is too high, there could plausibly be 1,500 minus 200, equals 1,300 red beads. If the estimate is too low, there could plausibly be 1,500 plus 200, equals 1,700 red beads. Therefore, the most plausible statement of the actual number of red beads in the bag is 1,300 is less than r, which is less than 1,700.

Choices A and D are incorrect and may result from misinterpreting the margin of error. It’s unlikely that more than 1,700 beads or fewer than 1,300 beads in the bag are red. Choice C is incorrect because 200 is the margin of error for the number of red beads, not the lower bound of the range of red beads.

 

Question 149 149 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

  • The data for the dot plot are as follows:
    • 1: 4 dots
    • 2: 5 dots
    • 3: 2 dots
    • 4: 1 dot
    • 5: 1 dot

 

The dot plot represents a data set of the number of bursts for 13 eruptions of a steam vent. If an additional eruption with 11 bursts is added to this data set to create a new data set of 14 eruptions, which of the following measures will be greater for the new data set than for the original data set?

  1. The median number of bursts
  2. The mean number of bursts
  1. I and II

  2. I only

  3. II only

  4. Neither I nor II

Show Answer Correct Answer: C

Choice C is correct. It’s given that the dot plot represents a data set of the number of bursts for 13 eruptions of a steam vent. The median of a data set with an odd number of elements is the middle element when the elements are in numerical order. For 13 elements in numerical order, this is the 7th element. For this data set, the first 4 elements have a value of 1 , and the next 5 elements have a value of 2 . Thus, the 7th element in the ordered data set is 2 and the median number of bursts for the original data set is 2 . If an additional eruption with 11 bursts is added to this data set to create a new data set of 14 eruptions, the median of the new data set will be between the 7th and 8th elements in the ordered set, which will also be 2 . Therefore, the median number of bursts for the new data set will be the same as the median number of bursts for the original data set. The mean number of bursts for the original data set is found by adding the values of all 13 elements and dividing that sum by the number of elements, 13 . Since the data is shown in a dot plot, the sum of the values of the elements can be found by multiplying each element's value by its frequency: 1(4)+2(5)+3(2)+4(1)+5(1), or 29 . Therefore, the mean number of bursts for the original data set is 2913. If an additional eruption with 11 bursts is added to this data set to create a new data set of 14 bursts, the mean number of bursts for the new data set is 29+1114, or 4014. Since 4014>2913, the mean number of bursts for the new data set is greater than the mean number of bursts for the original data set. Therefore, of the median number of bursts and the mean number of bursts, only the mean number of bursts is greater for the new data set than for the original data set.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 150 150 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M
Station 1 Station 2 Station 3 Station 4 Station 5
$3.699 $3.609 $3.729 $3.679 $3.729

In the table above, Melissa recorded the price of one gallon of regular gas from five different local gas stations on the same day. What is the median of the gas prices Melissa recorded?

  1. $3.679

  2. $3.689

  3. $3.699

  4. $3.729

Show Answer Correct Answer: C

Choice C is correct. The median of a data set is the middle value when the data is in ascending or descending order. In ascending order, the gas prices are $3.609, $3.679, $3.699, $3.729, and $3.729. The middle number of this list is 3.699, so it follows that $3.699 is the median gas price.

Choice A is incorrect. When the gas prices are listed in ascending order, this value isn’t the middle number. Choice B is incorrect. This value represents the mean gas price. Choice D is incorrect. This value represents both the mode and the maximum gas price.

Question 151 151 of 368 selected Percentages M

Which of the following represents the result of increasing the quantity x by 9%, where x is greater than 0 ?

  1. 1 point 0 9 x

  2. 0 point 0 9 x

  3. x plus 9

  4. x plus 0 point 0 9

Show Answer Correct Answer: A

Choice A is correct. Increasing the positive quantity x by 9% is the result of adding 9% of x to x. 9% of x can be represented algebraically as the fraction, 9 over 100, end fraction, times x, or 0 point 0 9 x. Adding this expression to x yields x plus 0 point 0 9 x, or 1 point 0 9 x.

Choice B is incorrect. This represents 9% of x. Choice C is incorrect. This represents increasing x by 9, not by 9%. Choice D is incorrect. This represents increasing x by 0.09, not by 9%.

 

Question 152 152 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

An object travels at a constant speed of 12 centimeters per second. At this speed, what is the time, in seconds, that it would take for the object to travel 108 centimeters?

  1. 9

  2. 96

  3. 120

  4. 972

Show Answer Correct Answer: A

Choice A is correct. If the object travels 108 centimeters at a speed of 12 centimeters per second, the time of travel can be determined by dividing the total distance by the speed. This results in 108 centimeters12 centimeters/second, which is 9 seconds.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 153 153 of 368 selected Percentages E

What is 20% of 440 ?

  1. 44

  2. 88

  3. 880

  4. 1,760

Show Answer Correct Answer: B

Choice B is correct. 20% of 440 can be calculated as (20100)(440), which is equivalent to 8,800100, or 88 .

Choice A is incorrect. This is 10%, not 20%, of 440 .

Choice C is incorrect. This is 200%, not 20%, of 440 .

Choice D is incorrect. This is 400%, not 20%, of 440 .

Question 154 154 of 368 selected Ratios, Rates, Proportional Relationships, And Units H
 
StatePower capacity
LowMediumHighTotal
Texas4239
California1012
Oregon1012
Indiana0202
Colorado1102
Iowa2002
Oklahoma1001
Total105520

The table shows the distribution, by location and power capacity (maximum rate of power generation) of the twenty largest wind projects in the United States in 2013. The total power capacity of the nine wind projects located in Texas was 4,952 megawatts (MW), and the total power capacity of the twenty wind projects was 11,037 MW in 2013. The amount of energy produced in one hour at a rate of one megawatt is one megawatt-hour. If each of the nine Texas wind projects in 2013 had operated continuously for 24 hours at the maximum rate of power generation, approximately how many megawatt-hours of energy would the nine projects have produced?

  1. 200

  2. 5,000

  3. 11,000

  4. 120,000

Show Answer Correct Answer: D

Choice D is correct. It’s given that the total power capacity of the nine wind projects in Texas was 4,952 megawatts. Therefore, if all nine Texas projects operated continuously for 1 hour, the amount of energy produced would be 4,952 megawatt-hours. It follows that, if all nine Texas projects operated continuously for 24 hours, the amount of energy produced, in megawatt-hours, would be 4,952 times 24, equals 118,848, which is closest to 120,000.

Choice A is incorrect. This is approximately the amount of energy produced for the nine projects divided by 24 hours. Choice B is incorrect. This is approximately the amount of energy produced for the nine projects. Choice C is incorrect. This is approximately the given amount of energy produced for all twenty projects in the table.

Question 155 155 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

If 4 a b = 6.7 and a b n = 26.8 , what is the value of n ?

Show Answer Correct Answer: .0625, 1/16

The correct answer is .0625. It's given that 4ab=6.7 and abn=26.8. The equation 4ab=6.7 can be rewritten as (4)(ab)=6.7. Dividing both sides of this equation by 4 yields ab=1.675. The equation abn=26.8 can be rewritten as (ab)(1n)=26.8. Substituting 1.675 for ab in this equation yields (1.675)(1n)=26.8, or 1.675n=26.8. Multiplying both sides of this equation by n yields 1.675=26.8n. Dividing both sides of this equation by 26.8 yields n=0.0625. Therefore, the value of n is 0.0625. Note that .0625, 0.062, 0.063, and 1/16 are examples of ways to enter a correct answer.

Question 156 156 of 368 selected Percentages M

The number k is 36% greater than 50. If k is the product of 50 and r, what is the value of ?

  1. 36

  2. 3.6

  3. 1.36

  4. 0.36

Show Answer Correct Answer: C

Choice C is correct. It’s given that the number k is 36% greater than 50. Therefore, the value of k is the number 50 plus 36% of 50. This can be rewritten as k equals, 50 plus, the fraction 36 over 100, end fraction, times 50. Multiplying the terms the fraction 36 over 100, end fraction, times 50 yields 18, so k equals, 50 plus 18, or k equals 68. It’s also given that k is the product of 50 and r, which can be rewritten as k equals 50 r. Substituting 68 for k yields 68 equals 50 r. Dividing both sides of this equation by 50 yields r equals 1 point 3 6.

Choice A is incorrect. This is the percentage that k is greater than 50. Choice B is incorrect and may result from a calculation error. Choice D is incorrect. This would be the value of r if k were 36% of 50, instead of 36% greater than 50.

 

Question 157 157 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

The weight of an object on Venus is approximately the fraction 9 over 10 of its weight on Earth. The weight of an object on Jupiter is approximately the fraction 23 over 10 of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus?

  1. 90
  2. 111
  3. 140
  4. 230
Show Answer Correct Answer: C

Choice C is correct. The weight of an object on Venus is approximately nine tenths of its weight on Earth. If an object weighs 100 pounds on Earth, then the object’s weight on Venus is approximately nine tenths times 100, equals 90 pounds. The same object’s weight on Jupiter is approximately twenty three tenths of its weight on Earth; therefore, the object weighs approximately twenty three tenths times 100, equals 230 pounds on Jupiter. The difference between the object’s weight on Jupiter and the object’s weight on Venus is approximately 230 minus 90, equals 140 pounds. Therefore, an object that weighs 100 pounds on Earth weighs 140 more pounds on Jupiter than it weighs on Venus.

Choice A is incorrect because it is the weight, in pounds, of the object on Venus. Choice B is incorrect because it is the weight, in pounds, of an object on Earth if it weighs 100 pounds on Venus. Choice D is incorrect because it is the weight, in pounds, of the object on Jupiter.

Question 158 158 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

For which of the following data sets is the mean greater than the median?

  1. 5, 5, 5, 5, 5, 5, 5, 5, 5

  2. 0, 10, 20, 30, 40, 50, 60, 70, 80

  3. 2, 4, 8, 16, 32, 64, 128, 256, 512

  4. 7, 107, 107, 207, 207, 207, 307, 307, 307

Show Answer Correct Answer: C

Choice C is correct. If the values in a data set are ordered from least to greatest, the median of the data set will be the middle value. Since each data set in the choices is ordered and contains exactly 9 data values, the 5th value in each is the median. It follows that the median of the data set in choice C is 32. The sum of the positive differences between 32 and each of the values that are less than 32 is significantly smaller than the sum of the positive differences between 32 and each of the values that are greater than 32. If 32 were the mean, these sums would have been equal to each other. Therefore, the mean of this data set must be greater than 32. This can also be confirmed by calculating the mean as the sum of the values divided by the number of values in the data set:  The fraction with numerator 2, plus 4, plus 8, plus 16, plus 32, plus 64, plus 128, plus 256, plus 512, and denominator 9, equals 113 and five ninths.

Choices A and B are incorrect. Each of the data sets in these choices is symmetric with respect to its median, so the mean and the median for each of these choices are equivalent. Choice D is incorrect. The median of this data set is 207. Since the sum of the positive differences between 207 and each of the values less than 207 is greater than the sum of the positive differences between 207 and each value greater than 207 in this data set, the mean must be less than the median.

Question 159 159 of 368 selected Probability And Conditional Probability H
 PhoneEmail
Dinner dance55%80%
Football game20%10%
Picnic20%5%
Pool party5%5%
Total100%100%

An alumni association survey asked each high school graduate to select the one activity he or she preferred for the association’s next event. Some of the people responded by phone, and the others responded by email. The table above shows the distribution of preferred activity, in percent, for each response type used. For the survey, the number of email responses was twice the number of phone responses. If a person who preferred a picnic is selected at random, what is the probability that the person responded by email?
Show Answer

The correct answer is one third. It’s given that the number of email responses is twice the number of phone responses. Therefore, if the number of phone responses is p, then the number of email responses is 2 p. The table shows that 20% of people who responded by phone preferred a picnic. It follows that the expression 0 point 2 0 p represents the number of these people. The table also shows that 5% of the people who responded by email preferred a picnic. The expression 0 point 0 5 times 2 p, or 0 point 1 p, represents the number of these people. Therefore, a total of 0 point 2 0 p plus 0 point 1 p, or 0 point 3 p people preferred a picnic. Thus, the probability of selecting at random a person who responded by email from the people who preferred a picnic is the fraction 0 point 1 p over 0 point 3 p, or one third. Note that 1/3, .3333, and 0.333 are examples of ways to enter a correct answer.

Question 160 160 of 368 selected Two-Variable Data: Models And Scatterplots M
The figure presents a scatterplot. The horizontal axis is labeled “High jump height, in feet,” and the numbers 0 through 6, in increments of 1, are indicated. The vertical axis is labeled “Long jump distance, in feet,” and the numbers 0 through 20, in increments of 2, are indicated. There are 20 dots indicated on the scatterplot. The dots begin in the lower left part of the plane, at the dot with coordinates 1 comma 2, and trend upward and to the right until they end in the upper right part of the plane, at the dot with coordinates 5 comma 15.

Each dot in the scatterplot above represents the height x, in feet, in the high jump, and the distance y, in feet, in the long jump, made by each student in a group of twenty students. The graph of which of the following equations is a line that most closely fits the data?

  1. y equals, 0 point 8 2 x, plus 3 point 3 0

  2. y equals, 0 point 8 2 x, minus 0 point 8 2

  3. y equals, 3 point 3 0 x, plus 0 point 8 2

  4. y equals, 3 point 3 0 x, minus 3 point 3 0

Show Answer Correct Answer: C

Choice C is correct. A line that most closely fits the data is a line with an approximately balanced number of data points above and below the line. Fitting a line to the data shown results in a line with an approximate slope of 3 and a y-intercept near the point with coordinates 0 comma 1. An equation for the line can be written in slope-intercept form, y equals, m x plus b, where m is the slope and b is the y-coordinate of the y-intercept. The equation y equals, 3 point 3 0 x plus 0 point 8 2 in choice C fits the data most closely.

Choices A and B are incorrect because the slope of the lines of these equations is 0.82, which is a value that is too small to be the slope of the line that fits the data shown. Choice D is incorrect. The graph of this equation has a y-intercept at the point with coordinates 0 comma negative 3 point 3 0, not the point with coordinates 0 comma 0 point 8 2. This line would lie below all of the data points, and therefore would not closely fit the data.

 

Question 161 161 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

The table shows the frequency of values in a data set.

Value Frequency
19 7
21 1
23 7
25 4

What is the minimum value of the data set?

Show Answer Correct Answer: 19

The correct answer is 19 . The minimum value of a data set is the least value in the data set. The frequency refers to the number of times a value occurs. The given table shows that for this data set, the value 19 occurs 7 times, the value 21 occurs 1 time, the value 23 occurs 7 times, and the value 25 occurs 4 times. Therefore, of the values 19 , 21 , 23 , and 25 given in the data set, the minimum value of the data set is 19 .

Question 162 162 of 368 selected Inference From Sample Statistics And Margin Of Error H
Sample Percent in favor Margin of error
A 52% 4.2%
B 48% 1.6%

The results of two random samples of votes for a proposition are shown above. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?

  1. Sample A had a smaller number of votes that could not be recorded.

  2. Sample A had a higher percent of favorable responses.

  3. Sample A had a larger sample size.

  4. Sample A had a smaller sample size.

Show Answer Correct Answer: D

Choice D is correct. Sample size is an appropriate reason for the margin of error to change. In general, a smaller sample size increases the margin of error because the sample may be less representative of the whole population.

Choice A is incorrect. The margin of error will depend on the size of the sample of recorded votes, not the number of votes that could not be recorded. In any case, the smaller number of votes that could not be recorded for sample A would tend to decrease, not increase, the comparative size of the margin of error. Choice B is incorrect. Since the percent in favor for sample A is the same distance from 50% as the percent in favor for sample B, the percent of favorable responses doesn’t affect the comparative size of the margin of error for the two samples. Choice C is incorrect. If sample A had a larger margin of error than sample B, then sample A would tend to be less representative of the population. Therefore, sample A is not likely to have a larger sample size.

Question 163 163 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

  • For the dot plot titled Class A:
    • The number line ranges from 1 to 7 in increments of 1.
    • The data for the dot plot are as follows:
      • 1: 1 dot
      • 2: 1 dot
      • 3: 3 dots
      • 4: 4 dots
      • 5: 5 dots
      • 6: 6 dots
      • 7: 7 dots
  • For the dot plot titled Class B:
    • The number line ranges from 14 to 20 in increments of 1.
    • The data for the dot plot are as follows:
      • 14: 1 dot
      • 15: 1 dot
      • 16: 3 dots
      • 17: 4 dots
      • 18: 5 dots
      • 19: 6 dots
      • 20: 7 dots

Each of the dot plots shown represents the number of glue sticks brought in by each student for two classes, class A and class B. Which statement best compares the standard deviations of the numbers of glue sticks brought in by each student for these two classes?

  1. The standard deviation of the number of glue sticks brought in by each student for class A is less than the standard deviation of the number of glue sticks brought in by each student for class B.

  2. The standard deviation of the number of glue sticks brought in by each student for class A is equal to the standard deviation of the number of glue sticks brought in by each student for class B.

  3. The standard deviation of the number of glue sticks brought in by each student for class A is greater than the standard deviation of the number of glue sticks brought in by each student for class B.

  4. There is not enough information to compare these standard deviations.

Show Answer Correct Answer: B

Choice B is correct. Standard deviation is a measure of the spread of a data set from its mean. The dot plot for class A and the dot plot for class B have the same shape. Thus, the frequency distributions for both class A and class B are the same. Since both class A and class B have the same frequency distribution of glue sticks brought in by each student, it follows that both class A and class B have the same spread of the number of glue sticks brought in by each student from their respective means. Therefore, the standard deviation of the number of glue sticks brought in by each student for class A is equal to the standard deviation of the number of glue sticks brought in by each student for class B.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 164 164 of 368 selected Percentages H

In 2008, Zinah earned 14% more than in 2007, and in 2009 Zinah earned 4% more than in 2008. If Zinah earned y times as much in 2009 as in 2007, what is the value of y ?

  1. 0.5600

  2. 1.0056

  3. 1.1800

  4. 1.1856

Show Answer Correct Answer: D

Choice D is correct. It’s given that in 2008 Zinah earned 14% more than in 2007. Let h represent the amount Zinah earned in 2007 and let j represent the amount that Zinah earned in 2008. This situation can be represented by the equation j=(1+14100)h, or j = 1.14 h . It’s also given that in 2009 Zinah earned 4% more than in 2008. Let k represent the amount Zinah earned in 2009. This situation can be represented by the equation k=(1+4100)j, or k=1.04j. Substituting 1.14 h for j in the equation k=1.04j yields k=(1.04)(1.14h), or k = 1.1856 h . If Zinah earned y times as much in 2009 as in 2007, then the value of y is 1.1856 .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 165 165 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

One of a planet's moons orbits the planet every 252 days. A second moon orbits the planet every 287 days. How many more days does it take the second moon to orbit the planet 29 times than it takes the first moon to orbit the planet 29 times?

Show Answer Correct Answer: 1015

The correct answer is 1,015 . It’s given that the first moon orbits the planet every 252 days. Therefore, it takes the first moon 252(29), or 7,308 , days to orbit the planet 29 times. It’s also given that the second moon orbits the planet every 287 days. Therefore, it takes the second moon 287(29), or 8,323 , days to orbit the planet 29 times. Since it takes the first moon 7,308 days and the second moon 8,323 days, it takes the second moon 8,323-7,308, or 1,015 , more days than it takes the first moon to orbit the planet 29 times.

Question 166 166 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

The density of a certain type of wood is 353  kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of 345 kilograms. To the nearest hundredth of a meter, what is the length of one edge of this sample? 

  1. 0.98

  2. 0.99

  3. 1.01

  4. 1.02

Show Answer Correct Answer: B

Choice B is correct. It’s given that the density of a certain type of wood is 353 kilograms per cubic meter (kg/m3), and a sample of this type of wood has a mass of 345 kg. Let x represent the volume, in m3, of the sample. It follows that the relationship between the density, mass, and volume of this sample can be written
as 353 kg1 m3=345 kgx m3, or 353=345x. Multiplying both sides of this equation by x yields 353x=345. Dividing both sides of this equation by 353 yields x=345353. Therefore, the volume of this sample is 345353 m3. Since it’s given that the sample of this type of wood is a cube, it follows that the length of one edge of this sample can be found using the volume formula for a cube, V=s3, where V represents the volume, in m3, and s represents the length, in m, of one edge of the cube. Substituting 345353for V in this formula yields 345353=s3. Taking the cube root of both sides of this equation yields 3453533=s, or s0.99. Therefore, the length of one edge of this sample to the nearest hundredth of a meter is 0.99 .

Choices A, C, and D are incorrect and may result from conceptual or calculation errors.

Question 167 167 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

How many feet are equivalent to 34 yards? (1 yard=3 feet)

Show Answer Correct Answer: 102

The correct answer is 102 . It’s given that 1 yard is equivalent to 3 feet. Therefore, 34 yards is equivalent to (34 yards)(3 feet1 yard), or 102  feet.

Question 168 168 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

A list of 10 data values is shown.

6 , 8 , 16 , 4 , 17 , 26 , 8 , 5 , 5 , 5

What is the mean of these data?

Show Answer Correct Answer: 10

The correct answer is 10 . The mean of a data set is calculated by dividing the sum of the data values by the number of data values in the data set. For this data set, the mean can be calculated as 6+8+16+4+17+26+8+5+5+510, which is equivalent to 10010, or 10 .

Question 169 169 of 368 selected Percentages H

The number a is 70% less than the positive number b . The number c is 80% greater than a . The number c is how many times b ?

Show Answer Correct Answer: .54, 27/50

The correct answer is .54. It's given that the number a is 70% less than the positive number b . Therefore, a=(1-70100)b, which is equivalent to a=(1-0.70)b, or a=0.30b. It's also given that the number c is 80% greater than a . Therefore, c=(1+80100)a, which is equivalent to c=(1+0.80)a, or c=1.80a. Since a = 0.30 b , substituting 0.30 b for a in the equation c = 1.80 a yields c=1.80(0.30b), or c=0.54b. Thus, c is 0.54 times b . Note that .54 and 27/50 are examples of ways to enter a correct answer.

Question 170 170 of 368 selected Inference From Sample Statistics And Margin Of Error M

From a population of 50,000 people, 1,000 were chosen at random and surveyed about a proposed piece of legislation. Based on the survey, it is estimated that 35 % of people in the population support the legislation, with an associated margin of error of 3 %. Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?

  1. 350

  2. 650

  3. 16,750

  4. 31,750

Show Answer Correct Answer: C

Choice C is correct. It’s given that an estimated 35% of people in the population support the legislation, with an associated margin of error of 3%. Subtracting and adding the margin of error from the estimate gives an interval of plausible values for the true percentage of people in the population who support the legislation. Therefore, it’s plausible that between 32% and 38% of people in this population support the legislation. The corresponding numbers of people represented by these percentages in the population can be calculated by multiplying the total population, 50,000 , by 0.32 and by 0.38 , which gives 50,000(0.32)=16,000 and 50,000(0.38)=19,000, respectively. It follows that any value in the interval 16,000 to 19,000 is a plausible value for the total number of people in the population who support the proposed legislation. Of the choices given, only 16,750 is in this interval.

Choice A is incorrect. This is the number of people in the sample, rather than in the population, who support the legislation.

Choice B is incorrect. This is the number of people in the sample who do not support the legislation.

Choice D is incorrect. This is a plausible value for the total number of people in the population who do not support the proposed legislation.

Question 171 171 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

6 , 6 , 8 , 8 , 8 , 10 , 21

Which of the following lists represents a data set that has the same median as the data set shown?

  1. 4 , 6 , 6 , 6 , 8 , 8

  2. 6 , 6 , 8 , 8 , 10 , 10

  3. 6 , 8 , 10 , 10 , 10 , 12

  4. 8 , 8 , 10 , 10 , 21 , 21

Show Answer Correct Answer: B

Choice B is correct. If a data set contains an odd number of data values, the median is represented by the middle data value in the list when the data values are listed in ascending or descending order. Since the data set shown has 7 data values and is in ascending order, it follows that the median is the fourth data value in the list, or 8 . If a data set contains an even number of data values, the median is between the two middle data values when the values are listed in ascending or descending order. Since each of the choices consists of a data set with 6 data values in ascending order, it follows that the median is between the third and fourth data value. The third and fourth data values in choice B are 8 and 8 . Thus, choice B represents a data set with a median of 8 . Since the median of the data set shown is 8 and choice B represents a data set with a median of 8 , it follows that choice B represents a data set that has the same median as the data set shown.

Choice A is incorrect. This list represents a data set with a median of 6 , not 8 .

Choice C is incorrect. This list represents a data set with a median of 10 , not 8 .

Choice D is incorrect. This list represents a data set with a median of 10 , not 8 .

Question 172 172 of 368 selected Two-Variable Data: Models And Scatterplots E
The figure presents a scatterplot titled “Density of Grape Juice.” The horizontal axis is labeled “Concentration,” and the percents 20 percent through 80 percent, in increments of 10 percent, are indicated. The vertical axis is labeled “Density, in kilograms per cubic meter,” and the numbers 1,000 through 1,400, in increments of 50, are indicated. There are 10 data points that begin in the lower left part of the scatterplot and trend upward and to the right. The data represented by the points are as follows. Note that all values are approximate.
Concentration, 23 percent. Density, 1,100 kilograms per cubic meter.
Concentration, 27 percent. Density, 1,110 kilograms per cubic meter.
Concentration, 32 percent. Density, 1,125 kilograms per cubic meter.
Concentration, 35 percent. Density, 1,150 kilograms per cubic meter.
Concentration, 42 percent. Density, 1,190 kilograms per cubic meter.
Concentration, 45 percent. Density, 1,210 kilograms per cubic meter.
Concentration, 51 percent. Density, 1,240 kilograms per cubic meter.
Concentration, 54 percent. Density, 1,260 kilograms per cubic meter.
Concentration, 67 percent. Density, 1,345 kilograms per cubic meter.
Concentration, 71 percent. Density, 1,360 kilograms per cubic meter.

The densities of different concentrations of grape juice are shown in the scatterplot above. According to the trend shown by the data, which of the following is closest to the predicted density, in kilograms per cubic meter (kg/m3), for grape juice with a concentration of 60%?

  1. 1,200

  2. 1,250

  3. 1,300

  4. 1,350

Show Answer Correct Answer: C

Choice C is correct. The data in the scatterplot show an increasing linear trend. The density when the juice concentration is 60% will be between the densities shown at about 53% and 67% concentration, or between about 1,255 and 1,340 kg/m3. Of the choices given, only 1,300 falls within this range.

Choices A, B, and D are incorrect. These are the approximate densities of grape juice with a concentration of 45%, 55%, and 70%, respectively.

Question 173 173 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments E

The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. Which of the following is true about the city council’s survey?

  1. It shows that the majority of city residents are in favor of the dog park.

  2. The survey sample should have included more residents who are dog owners.

  3. The survey sample should have consisted entirely of residents who do not own dogs.

  4. The survey sample is biased because it is not representative of all city residents.

Show Answer Correct Answer: D

Choice D is correct. The members of the city council wanted to assess opinions of all city residents. To gather an unbiased sample, the council should have used a random sampling design to select subjects from all city residents. The given survey introduced a sampling bias because the 500 city residents surveyed were all dog owners. This sample is not representative of all city residents because not all city residents are dog owners.

Choice A is incorrect because when the sampling method isn’t random, there is no guarantee that the survey results will be reliable; hence, they cannot be generalized to the entire population. Choice B is incorrect because a larger sample of residents who are dog owners would not correct the sampling bias. Choice C is incorrect because a survey sample of entirely non–dog owners would likely have a biased opinion, just as a sample of dog owners would likely have a biased opinion.

Question 174 174 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

The table below shows the high and low temperatures in Houston, Texas, during a five-day period.

The figure presents a 6-column table, with two rows of data, titled “Temperatures in Houston, Texas,” in degrees Fahrenheit. The first column has no heading. Columns 2 through 6 have the following headings: Monday, Tuesday, Wednesday, Thursday, and Friday, respectively. The 2 rows of data are as follows. 
Row 1. High temperature, in degrees Fahrenheit, for Monday through Friday, respectively: 73, 56, 62, 75, 81.
Row 2. Low temperature, in degrees Fahrenheit, for Monday through Friday, respectively: 49, 37, 41, 54, 63.

What was the mean low temperature, in degrees Fahrenheit, during the five-day period?

  1. 48.8

  2. 49

  3. 59

  4. 59.1

Show Answer Correct Answer: A

Choice A is correct. The mean low temperature can be calculated by finding the sum of the low temperatures for all the days shown in the table, 49 + 37 + 41 + 54 + 63 = 244, and then dividing the sum by the number of days the temperature was recorded, 244 divided by 5, equals 48 point 8.

Choice B is incorrect. This may be the result of choosing the median rather than calculating the mean. Choices C and D are incorrect and may be the result of calculation errors.

Question 175 175 of 368 selected Percentages H

210 is p% greater than 30 . What is the value of p ?

Show Answer Correct Answer: 600

The correct answer is 600 . It’s given that 210 is p% greater than 30 . It follows that 210=(1+p100)(30). Dividing both sides of this equation by 30 yields 7=1+p100. Subtracting 1 from both sides of this equation yields 6=p100. Multiplying both sides of this equation by 100 yields p = 600 . Therefore, the value of p is 600 .

Question 176 176 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

Data set A is the set consisting of the following seven numbers: 1 comma 2, comma 3, comma 4, comma 5, comma 6, comma 7.
Data set B is the set consisting of the following seven numbers: 1 comma 1, comma 2, comma 2, comma 3, comma 3, comma 4.

Which of the following statements correctly compares the means of data set A and data set B?

  1. The mean of each data set is 2.

  2. The mean of each data set is 4.

  3. The mean of data set A is less than the mean of data set B.

  4. The mean of data set A is greater than the mean of data set B.

Show Answer Correct Answer: D

Choice D is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is the fraction with numerator 1 plus 2, plus 3, plus 4, plus 5, plus 6, plus 7, and denominator 7, equals, the fraction 28 over 7, or 4. The mean of data set B is the fraction with numerator 1 plus 1, plus 2, plus 2, plus 3, plus 3, plus 4, and denominator 7, equals, the fraction 16 over 7, or approximately 2.2857. Therefore, the mean of data set A is greater than the mean of data set B.

Alternate approach: Data set A and data set B are both ordered from least to greatest value. Besides the first value in each data set, which is 1, each value in ordered data set B is less than the respective value in ordered data set A. Therefore, conceptually, the mean of data set A must be greater than the mean of data set B.

Choices A, B, and C are incorrect and may result from various misconceptions or miscalculations.

 

Question 177 177 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

Each of the following frequency tables represents a data set. Which data set has the greatest mean?

Show Answer Correct Answer: A

Choice A is correct. The tables in choices B, C, and D each represent a data set where the values 80 and 90 have the same frequency and the values 70 and 100 have the same frequency. It follows that each of these data sets is symmetric around the value halfway between 80 and 90 , or 85 . When a data set is symmetric around a value, that value is the mean of the data set. Therefore, the data sets represented by the tables in choices B, C, and D each have a mean of 85 . The table in choice A represents a data set where the value 90 has a greater frequency than the value 80 and the value 100 has a greater frequency than the value 70 . It follows that this data set has a mean greater than 85 . Therefore, of the given choices, choice A represents the data set with the greatest mean.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 178 178 of 368 selected Two-Variable Data: Models And Scatterplots E
The figure presents a line graph titled “Number of 3 D Movies Released by Year.” The horizontal axis is labeled “Year,” and the years 2003 through 2011 are indicated. The vertical axis is labeled “Number of 3 D movies released,” and the numbers 0 through 50, in increments of 10, are indicated. The data, represented by 9 points on the graph, are as follows. Note that all values are approximate.

2003, 2 movies.
2004, 2 movies.
2005, 6 movies.
2006, 8 movies.
2007, 6 movies.
2008, 8 movies.
2009, 20 movies.
2010, 26 movies.
2011, 46 movies.

According to the line graph above, between which two consecutive years was there the greatest change in the number of 3‑D movies released?

  1. 2003–2004

  2. 2008–2009

  3. 2009–2010

  4. 2010–2011

Show Answer Correct Answer: D

Choice D is correct. The change in the number of 3-D movies released between any two consecutive years can be found by first estimating the number of 3-D movies released for each of the two years and then finding the positive difference between these two estimates. Between 2003 and 2004, this change is approximately 2 minus 2, equals 0 movies; between 2008 and 2009, this change is approximately 20 minus 8, equals 12 movies; between 2009 and 2010, this change is approximately 26 minus 20, equals 6 movies; and between 2010 and 2011, this change is approximately 46 minus 26, equals 20 movies. Therefore, of the pairs of consecutive years in the choices, the greatest increase in the number of 3-D movies released occurred during the time period between 2010 and 2011.

Choices A, B, and C are incorrect. Between 2010 and 2011, approximately 20 more 3-D movies were released. The change in the number of 3-D movies released between any of the other pairs of consecutive years is significantly smaller than 20.

Question 179 179 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

23 , 27 , 27 , 32 , 35 , 36 , 52

What is the range of the 7 scores shown?

Show Answer Correct Answer: 29

The correct answer is 29 . The range of a data set is the difference between its maximum value and its minimum value. For the data set shown, the maximum score is 52 and the minimum score is 23 . The difference between those scores is 52-23, or 29 . Therefore, the range of the 7 scores shown is 29 .

Question 180 180 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

To make a bakery’s signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins? (1 pound = 16 ounces)

  1. 7.5

  2. 10

  3. 50.5

  4. 120

Show Answer Correct Answer: A

Choice A is correct. If 2.5 ounces of chocolate are needed for each muffin, then the number of ounces of chocolate needed to make 48 muffins is 48 times 2 point 5, equals 120 ounces. Since 1 pound = 16 ounces, the number of pounds that is equivalent to 120 ounces is120 over 16 equals 7 point 5 pounds. Therefore, 7.5 pounds of chocolate are needed to make the 48 muffins.

Choice B is incorrect. If 10 pounds of chocolate were needed to make 48 muffins, then the total number of ounces of chocolate needed would be 10 times 16, equals 160 ounces. The number of ounces of chocolate per muffin would then be160 over 48, equals 3 point 3 3 ounces per muffin, not 2.5 ounces per muffin. Choices C and D are also incorrect. Following the same procedures as used to test choice B gives 16.8 ounces per muffin for choice C and 40 ounces per muffin for choice D, not 2.5 ounces per muffin. Therefore, 50.5 and 120 pounds cannot be the number of pounds needed to make 48 signature chocolate muffins.

 

Question 181 181 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments H

A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia round and the number of hours that a team practices each week. For the study, the organizer selected 55 teams at random from all trivia teams in a certain tournament. The table displays the information for the 40 teams in the sample that practiced for at least 3 hours per week.

Hours practiced Number of points per round
6 to 13 points 14 or more points Total
3 to 5 hours 6 4 10
More than 5 hours 4 26 30
Total 10 30 40

Which of the following is the largest population to which the results of the study can be generalized?

  1. All trivia teams in the tournament that scored 14 or more points in the round

  2. The 55 trivia teams in the sample

  3. The 40 trivia teams in the sample that practiced for at least 3 hours per week

  4. All trivia teams in the tournament

Show Answer Correct Answer: D

Choice D is correct. It's given that the organizer selected 55 teams at random from all trivia teams in the tournament. A table is also given displaying the information for the 40 teams in the sample that practiced for at least 3 hours per week. Selecting a sample of a reasonable size at random to use for a survey allows the results from that survey to be applied to the population from which the sample was selected, but not beyond this population. Thus, only the sampling method information is necessary to determine the largest population to which the results of the study can be generalized. Since the organizer selected the sample at random from all trivia teams in the tournament, the largest population to which the results of the study can be generalized is all trivia teams in the tournament.

Choice A is incorrect. The sample was selected at random from all trivia teams in the tournament, not just from the teams that scored an average of 14 or more points per round.

Choice B is incorrect. If a study uses a sample selected at random from a population, the results of the study can be generalized to the population, not just the sample.

Choice C is incorrect. If a study uses a sample selected at random from a population, the results of the study can be generalized to the population, not just a subset of the sample.

Question 182 182 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

Each value in the data set shown represents the height, in centimeters, of a plant. 

6 , 10 , 13 , 2 , 15 , 22 , 10 , 4 , 4 , 4

What is the mean height, in centimeters, of these plants?

Show Answer Correct Answer: 9

The correct answer is 9 . The mean of a data set is the sum of the values in the data set divided by the number of values in the data set. It follows that the mean height, in centimeters, of these plants is the sum of the heights, in centimeters, of each plant, 6+10+13+2+15+22+10+4+4+4, or 90 , divided by the number of plants in the data set, 10 . Therefore, the mean height, in centimeters, of these plants is 9010, or 9

Question 183 183 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

Which of the following speeds is equivalent to 90 kilometers per hour? (1 kilometer = 1,000 meters)

  1. 25 meters per second

  2. 32 meters per second

  3. 250 meters per second

  4. 324 meters per second

Show Answer Correct Answer: A

Choice A is correct. Since 1 kilometer is equal to 1,000 meters, it follows that 90 kilometers is equal to 90 times 1,000, equals 90,000 meters. Since 1 hour is equal to 60 minutes and 1 minute is equal to 60 seconds, it follows that 1 hour is equal to 60 times 60, equals 3,600 seconds. Now the fraction 90 kilometers over 1 hour is equal to the fraction 90,000 meters over 3,600 seconds, which reduces to the fraction 25 meters over 1 second or 25 meters per second.

Choices B, C, and D are incorrect and may result from conceptual or calculation errors.

 

Question 184 184 of 368 selected Inference From Sample Statistics And Margin Of Error E

A certain forest is 253 acres. To estimate the number of trees in the forest, a ranger randomly selects 5 different 1-acre parcels in the forest and determines the number of trees in each parcel. The numbers of trees in the sample acres are 51, 59, 45, 52, and 73. Based on the mean of the sample, which of the following ranges contains the best estimate for the number of trees in the entire forest?

  1. 11,000 to 12,000

  2. 12,500 to 13,500

  3. 13,500 to 14,500

  4. 18,000 to 19,000

Show Answer Correct Answer: C

Choice C is correct. The mean of the 5 samples is the fraction with numerator, 51 plus 59 plus 45 plus 52 plus 73, and denominator 5, equals 56 trees per acre. The best estimate for the total number of trees in the forest is the product of the mean number of trees per acre in the sample and the total number of acres in the forest. This is (56)(253) = 14,168, which is between 13,500 and 14,500.

Choice A is incorrect and may result from multiplying the minimum number of trees per acre in the sample, 45, by the number of acres, 253. Choice B is incorrect and may result from multiplying the median number of trees per acre in the sample, 52, by the number of acres, 253. Choice D is incorrect and may result from multiplying the maximum number of trees per acre in the sample, 73, by the number of acres, 253.

 

Question 185 185 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E
The figure presents a box plot titled “Acres of useful timberland.” The numbers 1,000 through 14,000, in increments of 1,000, are indicated on the horizontal axis. The data represented by the box plot are as follows. Note that all values are approximate. In the box plot, the left whisker extends from 1,100 to 4,500; the box extends from 4,500 to 10,500; a vertical line segment at 7,100 divides the box into 2 parts; and the right whisker extends from 10,500 to 13,300.

The number of acres of useful timberland in 13 counties in California is summarized in the box plot above. Which of the following is closest to the median number of acres?

  1. 4,399

  2. 7,067

  3. 8,831

  4. 10,595

Show Answer Correct Answer: B

Choice B is correct. The median of the data summarized by a box plot is the value associated with the vertical line segment within the box. According to the box plot shown, this value is slightly greater than 7,000. Therefore, the closest value for the median number of acres is 7,067.

Choice A is incorrect. This is the value associated with the vertical line segment forming the left-hand side of the box. Choice C is incorrect. This value is greater than the value associated with the vertical line segment within the box. Choice D is incorrect. This is the value associated with the vertical line segment forming the right-hand side of the box.

Question 186 186 of 368 selected Probability And Conditional Probability H

On May 10, 2015, there were 83 million Internet subscribers in Nigeria. The major Internet providers were MTN, Globacom, Airtel, Etisalat, and Visafone. By September 30, 2015, the number of Internet subscribers in Nigeria had increased to 97 million. If an Internet subscriber in Nigeria on September 30, 2015, is selected at random, the probability that the person selected was an MTN subscriber is 0.43. There were p million MTN subscribers in Nigeria on September 30, 2015. To the nearest integer, what is the value of p ?

Show Answer

The correct answer is 42. It’s given that in Nigeria on September 30, 2015, the probability of selecting an MTN subscriber from all Internet subscribers is 0.43, that there were p million, or p of 1,000,000, MTN subscribers, and that there were 97 million, or 97,000,000, Internet subscribers. The probability of selecting an MTN subscriber from all Internet subscribers can be found by dividing the number of MTN subscribers by the total number of Internet subscribers. Therefore, the equation the fraction with numerator p of 1,000,000, and denominator 97,000,000, equals 0 point 4 3 can be used to solve for p. Dividing 1,000,000 from the numerator and denominator of the expression on the left-hand side yields the fraction p over 97, equals 0 point 4 3. Multiplying both sides of this equation by 97 yields p equals, 0 point 4 3 times 97, which equals 41 point 7 1, which, to the nearest integer, is 42.

Question 187 187 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7 years. After one of the employees leaves the company, the mean amount of time that the remaining employees have worked for the company is reduced to 6.25 years. How many years did the employee who left the company work for the company?

  1. 0.45

  2. 2.30

  3. 9.00

  4. 15.25

Show Answer Correct Answer: D

Choice D is correct. The mean amount of time that the 20 employees worked for the company is 6.7 years. This means that the total number of years all 20 employees worked for the company is (6.7)(20) = 134 years. After the employee left, the mean amount of time that the remaining 19 employees worked for the company is 6.25 years. Therefore, the total number of years all 19 employees worked for the company is (6.25)(19) = 118.75 years. It follows that the number of years that the employee who left had worked for the company is 134 – 118.75 = 15.25 years.

Choice A is incorrect; this is the change in the mean, which isn’t the same as the amount of time worked by the employee who left. Choice B is incorrect and likely results from making the assumption that there were still 20 employees, rather than 19, at the company after the employee left and then subtracting the original mean of 6.7 from that result. Choice C is incorrect and likely results from making the assumption that there were still 20 employees, rather than 19, at the company after the employee left.

Question 188 188 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

A distance of 61 furlongs is equivalent to how many feet? (1 furlong=220 yards and 1 yard=3 feet)

Show Answer Correct Answer: 40260

The correct answer is 40,260 . It's given that 1 furlong=220 yards and 1 yard=3 feet. It follows that a distance of 61 furlongs is equivalent to (61 furlongs)(220 yards1 furlong)(3 feet1 yard), or 40,260 feet.

Question 189 189 of 368 selected Ratios, Rates, Proportional Relationships, And Units M
Food Protein  Cost
1 large egg 6 grams $0.36
1 cup of milk 8 grams $0.24

The table above shows the amount of protein in two foods and the cost of each food. Based on the table, what is the ratio of the cost per gram of protein in a large egg to the cost per gram of protein in a cup of milk?

  1. 1 : 2

  2. 2 : 3

  3. 3 : 4

  4. 2 : 1

Show Answer Correct Answer: D

Choice D is correct. The cost per gram of protein in 1 large egg is $0.36 ÷ 6 = $0.06. The cost per gram of protein in 1 cup of milk is $0.24 ÷ 8 = $0.03. It follows that the ratio of the cost per gram of protein in a large egg to the cost per gram of protein in a cup of milk is 0.06:0.03, which can be rewritten as 2:1.

Choice A is incorrect and may result from finding the ratio of the cost per gram of protein in a cup of milk to the cost per gram of protein in a large egg (the reciprocal of the ratio specified in the question). Choices B and C are incorrect and may result from incorrectly calculating the unit rates or from errors made when simplifying the ratio.

Question 190 190 of 368 selected Two-Variable Data: Models And Scatterplots H

The scatterplot shows the relationship between the length of time y , in hours, a certain bird spent in flight and the number of days after January 11 , x .

  • The scatterplot has 10 data points.
  • The data points are spread out.
  • The data points have the following coordinates:
    • (1 comma 14)
    • (2 comma 6)
    • (3 comma 10)
    • (4 comma 15)
    • (5 comma 14.2)
    • (6 comma 7)
    • (7 comma 11)
    • (8 comma 14)
    • (9 comma 13.5)
    • (10 comma 13.2)

What is the average rate of change, in hours per day, of the length of time the bird spent in flight on January 13 to the length of time the bird spent in flight on January 15 ?

Show Answer Correct Answer: 4.5, 9/2

The correct answer is 9 2 . It's given that the scatterplot shows the relationship between the length of time y , in hours, a certain bird spent in flight and the number of days after January 11 , x . Since January 13 is 2 days after January 11 , it follows that January 13 corresponds to an x-value of 2 in the scatterplot. In the scatterplot, when x = 2 , the corresponding value of y is 6 . In other words, on January 13 , the bird spent 6 hours in flight. Since January 15 is 4 days after January 11 , it follows that January 15 corresponds to an x-value of 4 in the scatterplot. In the scatterplot, when x = 4 , the corresponding value of y is 15 . In other words, on January 15 , the bird spent 15 hours in flight. Therefore, the average rate of change, in hours per day, of the length of time the bird spent in flight on January 13 to the length of time the bird spent in flight on January 15 is the difference in the length of time, in hours, the bird spent in flight divided by the difference in the number of days after January 11 , or 15-64-2, which is equivalent to 9 2 . Note that 9/2 and 4.5 are examples of ways to enter a correct answer.

Question 191 191 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments H

A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students’ accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game showed significant improvement in accuracy when adding fractions. What is the largest group to which the results of the study can be generalized?

  1. The 35 students in the sample

  2. All students at the school

  3. All middle school students in the city

  4. All students in the city

Show Answer Correct Answer: B

Choice B is correct. The largest group to which the results of a study can be generalized is the population from which the random sample was chosen. In this case, the psychologist chose a random sample from all students at one particular middle school. Therefore, the largest group to which the results can be generalized is all the students at the school.

Choice A is incorrect because this isn’t the largest group the results can be generalized to. Choices C and D are incorrect because these groups are larger than the population from which the random sample was chosen. Therefore, the sample isn’t representative of these groups.

 

Question 192 192 of 368 selected Probability And Conditional Probability E

A store received a shipment of 1,000 MP3 players, 4 of which were defective. If an MP3 player is randomly selected from this shipment, what is the probability that it is defective?

  1. 0.004

  2. 0.04

  3. 0.4

  4. 4

Show Answer Correct Answer: A

Choice A is correct. The probability of randomly selecting a defective MP3 player from the shipment is equal to the number of defective MP3 players divided by the total number of MP3 players in the shipment. Therefore, the probability is 4 over 1,000, which is equivalent to 0.004.

Choice B is incorrect because 0.04 represents 4 defective MP3 players out of 100 rather than out of 1,000. Choice C is incorrect because 0.4 represents 4 defective MP3 players out of 10 rather than out of 1,000. Choice D is incorrect. This is the number of defective MP3 players in the shipment.

 

Question 193 193 of 368 selected Percentages M

The value of z is 1.13 times 100 . The value of z is what percent greater than 100 ?

  1. 11.3

  2. 13

  3. 130

  4. 213

Show Answer Correct Answer: B

Choice B is correct. It’s given that the value of z is 1.13 times 100 . This can be written as z=(1.13)(100), which is equivalent to z=(1+0.13)(100), or z=(1+13100)(100). It follows that the value of z is 100% of 100 plus 13% of 100 . Therefore, the value of z is 13% greater than 100 .

Choice A is incorrect. This gives a value of z that is 1.113 , not 1.13 , times 100 .

Choice C is incorrect. This gives a value of z that is 2.30 , not 1.13 , times 100 .

Choice D is incorrect. This gives a value of z that is 3.13 , not 1.13 , times 100 .

Question 194 194 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments M

A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?

  1. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.
  2. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
  3. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

  1. None

  2. II only

  3. I and II only

  4. I and III only

Show Answer Correct Answer: A

Choice A is correct. Statement I need not be true. The fact that 78% of the 1,000 adults who were surveyed responded that they were satisfied with the air quality in the city does not mean that the exact same percentage of all adults in the city will be satisfied with the air quality in the city. Statement II need not be true because random samples, even when they are of the same size, are not necessarily identical with regard to percentages of people in them who have a certain opinion. Statement III need not be true for the same reason that statement II need not be true: results from different samples can vary. The variation may be even bigger for this sample since it would be selected from a different city. Therefore, none of the statements must be true.

Choices B, C, and D are incorrect because none of the statements must be true.

Question 195 195 of 368 selected Inference From Sample Statistics And Margin Of Error E

At a large high school, 300 students were selected at random and were asked in a survey about a menu change in the school cafeteria. All 300 students completed the survey. It was estimated that 38% of the students were in support of a menu change, with a margin of error of 5.5%. Which of the following is the best interpretation of the survey results?

  1. The percent of the students at the school who support a menu change is 38%.

  2. The percent of the students at the school who support a menu change is greater than 38%.

  3. Plausible values of the percent of the students at the school who support a menu change are between 32.5% and 43.5%.

  4. Plausible values of the number of the students at the school who support a menu change are between 295 and 305.

Show Answer Correct Answer: C

Choice C is correct. It’s given that an estimated 38% of sampled students at the school were in support of a menu change, with a margin of error of 5.5%. It follows that the percent of the students at the school who support a menu change is 38% plus or minus 5.5%. The lower bound of this estimation is 38 minus 5 point 5, or 32.5%. The upper bound of this estimation is 38 plus 5 point 5, or 43.5%. Therefore, plausible values of the percent of the students at the school who support a menu change are between 32.5% and 43.5%.

Choice A is incorrect. This is the percent of the sampled students at the school who support a menu change. Choices B and D are incorrect and may result from misinterpreting the margin of error.

 

Question 196 196 of 368 selected Percentages E

The length of the base of a certain parallelogram is 89% of the height of the parallelogram. Which expression represents the length of the base of the parallelogram, where h is the height of the parallelogram?

  1. 89 h

  2. 0.089 h

  3. 8.9 h

  4. 0.89 h

Show Answer Correct Answer: D

Choice D is correct. It's given that the length of the base of the parallelogram is 89% of the height of the parallelogram. Since h is the height of the parallelogram, it follows that the length of the base of the parallelogram can be represented by the expression 89100h, or 0.89 h .

Choice A is incorrect. This expression represents 8,900%, not 89%, of the height of the parallelogram.

Choice B is incorrect. This expression represents 8.9%, not 89%, of the height of the parallelogram.

Choice C is incorrect. This expression represents 890%, not 89%, of the height of the parallelogram.

Question 197 197 of 368 selected Percentages E
The figure presents a 2-column table, with 6 rows of data, titled “Where Do People Get Most of Their Medical Information?” The heading for the first column is “Source,” and the heading for the second column is “Percent of those surveyed.” The 6 rows of data are as follows. 
Row 1. Doctor, 63 percent.
Row 2. Internet, 13 percent.
Row 3. Magazines / brochures, 9 percent.
Row 4. Pharmacy, 6 percent.
Row 5. Television, 2 percent.
Row 6. Other / none of the above, 7 percent.

The table above shows a summary of 1,200 responses to a survey question. Based on the table, how many of those surveyed get most of their medical information from either a doctor or the Internet?

  1. 865

  2. 887

  3. 912

  4. 926

Show Answer Correct Answer: C

Choice C is correct. According to the table, 63% of survey respondents get most of their medical information from a doctor and 13% get most of their medical information from the Internet. Therefore, 76% of the 1,200 survey respondents get their information from either a doctor or the Internet, and 76% of 1,200 is 912.

Choices A, B, and D are incorrect. According to the table, 76% of survey respondents get their information from either a doctor or the Internet. Choice A is incorrect because 865 is about 72% (the percent of survey respondents who get most of their medical information from a doctor or from magazines/brochures), not 76%, of 1,200. Choice B is incorrect because 887 is about 74%, not 76%, of 1,200. Choice D is incorrect because 926 is about 77%, not 76%, of 1,200.

Question 198 198 of 368 selected Probability And Conditional Probability M

For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results are summarized in the table below.

Weekday and Weekend Day Rain for 12 Weeks
Rain No rain Total
Number of weekdays 12 48 60
Number of weekend days 8 16 24
Total 20 64 84

If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?

  1. the fraction 4 over 21
  2. the fraction 1 over 4
  3. the fraction 2 over 3
  4. the fraction 3 over 4
Show Answer Correct Answer: B

Choice B is correct. There were 64 days with no rain. It was a weekend day for 16 of those 64 days. So 16 out of 64 of the days with no rain were weekend days. Because the day is selected at random, each day has an equal chance of being selected, so the probability is the fraction 16 over 64, equals the fraction 1 over 4.

Choice A is incorrect. It is the probability that a day selected at random from any one of the days during the 12 weeks is a weekend day with no rain. Choice C is incorrect. It is the probability that a day selected at random from the weekend days has no rain. Choice D is incorrect. It is the probability that a day selected at random from the days with no rain is a weekday.

Question 199 199 of 368 selected Percentages E

Of 900,000 beads, 828,000 are silver. What percentage of the beads are silver?

  1. 8 %

  2. 36 %

  3. 72 %

  4. 92 %

Show Answer Correct Answer: D

Choice D is correct. The proportion of the beads that are silver can be written as 828,000900,000, or 0.92 . Therefore, the percentage of the beads that are silver is 0.92(100), or 92%.

Choice A is incorrect. This is the percentage of the beads that are not silver.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 200 200 of 368 selected Two-Variable Data: Models And Scatterplots M

  • The scatterplot has 11 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • 5 points are above the line of best fit.
    • 6 points are below the line of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (2 comma 2.9)
      • (8 comma 7.7)

The scatterplot shows the relationship between two variables, x and y . A line of best fit is also shown. For how many of the 11 data points does the line of best fit predict a greater y -value than the actual y -value?

Show Answer Correct Answer: 6

The correct answer is 6 . The line of best fit predicts a greater y-value than the actual y-value for any data point that's located below the line of best fit. For the scatterplot shown, 6 of the data points are below the line of best fit. Therefore, the line of best fit predicts a greater y-value than the actual y-value for 6 of the data points.

Question 201 201 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A fish swam a distance of 5,104 yards. How far did the fish swim, in miles(1 mile=1,760 yards) 

  1. 0.3

  2. 2.9

  3. 3,344

  4. 6,864

Show Answer Correct Answer: B

Choice B is correct. It’s given that the fish swam 5,104 yards and that 1 mile is equal to 1,760 yards. Therefore, the fish swam 5,104 yards(1 mile1,760 yards), which is equivalent to 5,1041,760 miles, or 2.9 miles. 

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 202 202 of 368 selected Percentages E

There are 250 trees in a park. Of these trees, 6% are birch trees. How many birch trees are in the park?

  1. 6

  2. 15

  3. 75

  4. 244

Show Answer Correct Answer: B

Choice B is correct. It's given that there are 250 trees in a park and of these trees, 6% are birch trees. The number of birch trees in the park can be calculated by multiplying the number of trees in the park by 6100. Therefore, the number of birch trees in the park is 250(6100), or 15 .

Choice A is incorrect. This is the percentage of trees in the park that are birch trees, not the number of birch trees in the park.

Choice C is incorrect. This is 30%, not 6%, of 250 .

Choice D is incorrect and may result from conceptual or calculation errors.

Question 203 203 of 368 selected Percentages M

The population of Greenville increased by 7 % from 2015 to 2016. If the 2016 population is k times the 2015 population, what is the value of k ?

  1. 0.07

  2. 0.7

  3. 1.07

  4. 1.7

Show Answer Correct Answer: C

Choice C is correct. Let x be the 2015 population of Greenville. It's given that the population increased by 7% from 2015 to 2016. The increase in population can be written as (0.07)x. The 2016 population of Greenville is given as the sum of the 2015 population of Greenville and the increase in population from 2015 to 2016. This can be rewritten as x+(0.07)x, or 1.07x. Therefore, the value of k is 1.07 .

Choice A is incorrect. This is the percent, represented as a decimal, that the population increased from 2015 to 2016, not the value of k .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the value of k if the population increased by 70%, not 7%, from 2015 to 2016.

Question 204 204 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

The population density of Cedar County is 230 people per square mile. The county has a population of 85,100 people. What is the area, in square miles, of Cedar County?

Show Answer Correct Answer: 370

The correct answer is 370 . It’s given that the population density of Cedar County is 230 people per square mile and the county has a population of 85,100 people. Based on the population density, it follows that the area of Cedar County is (85,100 people)(1 square mile230 people), or 370 square miles.

Question 205 205 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the relationship between two variables, x and y .

  • The scatterplot has 5 data points.
  • The data points are in a linear pattern trending up from left to right.
  • The data points have the following coordinates:
    • (1 comma 3.0)
    • (3 comma 5.0)
    • (5 comma 6.0)
    • (7 comma 8.0)
    • (9 comma 10.0)

Which equation is the most appropriate linear model for this relationship?

  1. y = - 0.9 x - 2.2

  2. y = - 0.9 x + 2.2

  3. y = - 0.9 x

  4. y = 0.9 x + 2.2

Show Answer Correct Answer: D

Choice D is correct. A linear model can be written in the form y = m x + b , where m is the slope of the graph of the model in the xy-plane and (0,b) is the y-intercept. The graph of an appropriate linear model for this relationship passes near the points (1,3) and (9,10) in the xy-plane. Two points on a line, (x1,y1) and (x2,y2), can be used to find the slope of the line using the slope formula, m=y2-y1x2-x1. Substituting the points (1,3) and (9,10) for (x1,y1) and (x2,y2), respectively, in the slope formula yields m=10-39-1, or m=0.875. Therefore, the value of m for an appropriate linear model is approximately 0.875. Substituting 0.875 for m in y = m x + b yields y=0.875x+b. Since an appropriate linear model passes near the point (1,3), the approximate value of b can be found by substituting 1 for x and 3 for y in the equation y=0.875x+b, which yields 3=(0.875)(1)+b, or 3=0.875+b. Subtracting 0.875 from both sides of this equation yields 2.125=b. Therefore, the value of b for an appropriate linear model is approximately 2.125. Thus, of the given choices, y=0.9x+2.2 is the most appropriate linear model for this relationship.

Alternate approach: A linear model can be written in the form y = m x + b , where m is the slope of the graph of the model in the xy-plane and (0,b) is the y-intercept. The scatterplot shows that as the x-values of the data points increase, the y-values of the data points increase, which means the graph of an appropriate linear model has a positive slope. Of the given choices, y=0.9x+2.2 is the only linear model whose graph has a positive slope.

Choice A is incorrect. The graph of this model has a negative slope, not a positive slope. 

Choice B is incorrect. The graph of this model has a negative slope, not a positive slope.

Choice C is incorrect. The graph of this model has a negative slope, not a positive slope.

Question 206 206 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

What length, in centimeters, is equivalent to a length of 51 meters? (1 meter=100 centimeters)

  1. 0.051

  2. 0.51

  3. 5,100

  4. 51,000

Show Answer Correct Answer: C

Choice C is correct. Since 1 meter is equal to 100 centimeters, 51 meters is equal to 51 meters(100 centimeters1 meter), or 5,100 centimeters. 

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from dividing, rather than multiplying, 51 by 100 .

Choice D is incorrect. This is the length, in millimeters rather than centimeters, that is equivalent to a length of 51 meters. 

Question 207 207 of 368 selected Probability And Conditional Probability H

The table summarizes the distribution of age and assigned group for 90 participants in a study.

  0 9 years 10 19 years 20+ years Total
Group A 7 14 9 30
Group B 6 4 20 30
Group C 17 12 1 30
Total 30 30 30 90

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age? (Express your answer as a decimal or fraction, not as a percent.)

Show Answer Correct Answer: .3833, 23/60

The correct answer is 23 60 . It's given that one of the participants will be selected at random. The probability of selecting a participant from group A given that the participant is at least 10 years of age is the number of participants in group A who are at least 10 years of age divided by the total number of participants who are at least 10 years of age. The table shows that in group A, there are 14 participants who are 10 19 years of age and 9 participants who are 20+ years of age. Therefore, there are 14+9, or 23 , participants in group A who are at least 10 years of age. The table also shows that there are a total of 30 participants who are 10 19 years of age and 30 participants who are 20+ years of age. Therefore, there are a total of 30+30, or 60 , participants who are at least 10 years of age. It follows that the probability of selecting a participant from group A given that the participant is at least 10 years of age is 23 60 . Note that 23/60, .3833, and 0.383 are examples of ways to enter a correct answer.

Question 208 208 of 368 selected Percentages M

In a group, 40 % of the items are red. Of all the red items in the group, 30 % also have stripes. What percentage of the items in the group are red with stripes?

  1. 10 %

  2. 12 %

  3. 70 %

  4. 75 %

Show Answer Correct Answer: B

Choice B is correct. It’s given that in a group, 40% of the items are red. It follows that the number of red items in the group can be represented by 0.4x, where x represents the total number of items in the group. It’s also given that of all the red items in the group, 30% also have stripes. It follows that the number of items in the group that are red and have stripes can be represented by 0.3(0.4x), or 0.12x. The expression 0.12x represents 12% of x . Since x represents the total number of items in the group, it follows that 12% of the items in the group are red and have stripes.

Choice A is incorrect and may result from subtracting 30% from 40% rather than calculating 30% of 40%.

Choice C is incorrect and may result from adding 30% and 40% rather than calculating 30% of 40%.

Choice D is incorrect and may result from calculating the percentage that 30% is of 40% rather than calculating 30% of 40%.

Question 209 209 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

A certain town has an area of 4.36 square miles. What is the area, in square yards, of this town? (1 mile=1,760 yards)

  1. 404

  2. 7,674

  3. 710,459

  4. 13,505,536

Show Answer Correct Answer: D

Choice D is correct. Since the number of yards in 1 mile is 1,760 , the number of square yards in 1 square mile is (1,760)(1,760)=3,097,600. Therefore, if the area of the town is 4.36 square miles, it is 4.36(3,097,600)=13,505,536, in square yards.

Choice A is incorrect and may result from dividing the number of yards in a mile by the square mileage of the town.

Choice B is incorrect and may result from multiplying the number of yards in a mile by the square mileage of the town.

Choice C is incorrect and may result from dividing the number of square yards in a square mile by the square mileage of the town.

Question 210 210 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

A study was conducted on the production rates for a company that produces tractor wheels. The table below shows the number of wheels made during 11 consecutive one-hour production periods.

One-hour
period
Number
of wheels
made
A24
B24
C21
D21
E21
F19
G24
H24
I19
J22
K23

What is the range of the number of wheels made for the 11 one-hour periods?

  1. 5.5

  2. 5.0

  3. 4.5

  4. 4.0

Show Answer Correct Answer: B

Choice B is correct. Range is defined as the difference between the greatest and least values from a set of data. The greatest number of wheels made during a one-hour period was 24 wheels. The least number of wheels was 19. Hence, the range is 24 minus 19, equals 5, or 5.0.

Choices A, C, and D are incorrect and may be the result of arithmetic errors or incorrectly identifying the greatest or least number of wheels made during a one-hour period.

Question 211 211 of 368 selected Two-Variable Data: Models And Scatterplots M
The figure presents a scatterplot titled “Railroad Museum Visitors.” The horizontal axis is labeled “Years since 1968,” and the numbers 0 through 15, in increments of 5, are indicated. The vertical axis is labeled “Annual visitors,” and the numbers 0 through 80,000, in increments of 20,000, are indicated. There are 13 data points indicated on the scatterplot. The data points begin at the point with approximate coordinates 0 comma 5,000, and trend upward and to the right until they end at the point with approximate coordinates 12 comma 75,000. A line of best fit is drawn. The line begins at the point with approximate coordinates 0 comma 16,000, and slants upward and to the right. It passes through the point with approximate coordinates 5 comma 40,000, and continues upward until it ends at the point with approximate coordinates 12 comma 74,000.

The scatterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where t is the number of years since 1968 and n is the number of visitors. A line of best fit is also shown. Which of the following could be an equation of the line of best fit shown?

  1. n equals, 16,090, plus 4,680, t

  2. n equals, 4,690, plus 16,090, t

  3. n equals, 16,090, plus 9,060, t

  4. n equals, 9,060, plus 16,090, t

Show Answer Correct Answer: A

Choice A is correct. An equation of a line of best fit can be written in the form y equals, a, plus b x, where a is the y-intercept of the line and b is the slope. In the scatterplot shown, the line of best fit intersects the y-axis just over halfway between 10,000 and 20,000, or approximately 16,000. The line of best fit also intersects the graph at the point with coordinates 5 comma 40,000 . Using the slope formula b equals, the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction and two points that lie on the graph such as the point with coordinates 5 comma 40,000 and the point with coordinates 0 comma 16,000 , the slope can be approximated as the fraction with numerator 40,000 minus 16,000, and denominator 5 minus 0, end fraction, or 4,800. Only choice A has a y-intercept near the estimate of 16,000 and a slope near the estimate of 4,800. Therefore, an equation of the line of best fit could be n equals, 16,090 plus 4,680 t.

Choice B is incorrect because the values for the slope and the y-coordinate of the y-intercept are switched. Choice C is incorrect because the value for the slope is approximately double the actual slope. Choice D is incorrect because the values for the slope and the y-intercept are switched and because the slope is approximately double the actual slope.

 

Question 212 212 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

A distance of 112 furlongs is equivalent to how many feet? (1 furlong=220 yards and 1 yard=3 feet)

Show Answer Correct Answer: 73920

The correct answer is 73,920 . It's given that 1 furlong=220 yards and 1 yard=3 feet. It follows that a distance of 112 furlongs is equivalent to (112 furlongs)(220 yards1 furlong)(3 feet1 yard), or 73,920 feet.

Question 213 213 of 368 selected Percentages M

A number n is increased 6%. If the result is 318, what is the value of n ?

  1. 199

  2. 299

  3. 300

  4. 337

Show Answer Correct Answer: C

Choice C is correct. The decimal equivalent of 6% is 0.06. Since increasing the number n by 6% yields the number 318, this situation can be represented by the equation n  times, open parenthesis, 1 plus 0 point 0 6, close parenthesis, equals 318, or n times 1 point 0 6, equals 318. Dividing both sides of this equation by 1.06 yields n equals 300.

Choice A is incorrect. This is the result when n is increased by 60%, not by 6%. Choice B is incorrect. This is the approximate result of decreasing 318 by 6%. Choice D is incorrect. This is the approximate result of increasing 318 by 6%.

 

Question 214 214 of 368 selected Percentages H

The result of increasing the quantity x by 400 % is 60 . What is the value of x ?

  1. 12

  2. 15

  3. 240

  4. 340

Show Answer Correct Answer: A

Choice A is correct. It's given that the result of increasing the quantity x by 400% is 60 . This can be written as x+(400100)x=60, which is equivalent to x+4x=60, or 5 x = 60 . Dividing each side of this equation by 5 yields x = 12 . Therefore, the value of x is 12 .

Choice B is incorrect. The result of increasing the quantity 15 by 400% is 75 , not 60 .

Choice C is incorrect. The result of increasing the quantity 240 by 400% is 1,200 , not 60 .

Choice D is incorrect. The result of increasing the quantity 340 by 400% is 1,700 , not 60 .

Question 215 215 of 368 selected Two-Variable Data: Models And Scatterplots E

  • The scatterplot has 12 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • The line of best fit passes through the following approximate coordinates:
      • (600 comma 5.6)
      • (1,200 comma 11.0)
      • (1,500 comma 13.8)
      • (1,800 comma 16.5)

Twelve data points are shown in the scatterplot. A line of best fit for the data is also shown. At x=1,200, which of the following is closest to the y-value predicted by the line of best fit?

  1. 16

  2. 14

  3. 11

  4. 6

Show Answer Correct Answer: C

Choice C is correct. On the line of best fit, an x-value of 1,200 corresponds to a y-value between 10 and 12 . Therefore, of the given choices, 11 is closest to the y-value predicted by the line of best fit at x=1,200.

Choice A is incorrect. This is the integer value closest to the y-value predicted by the line of best fit at x=1,800.

Choice B is incorrect. This is the integer value closest to the y-value predicted by the line of best fit at x=1,500.

Choice D is incorrect. This is the integer value closest to the y-value predicted by the line of best fit at x=600.

Question 216 216 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments E

A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?

  1. At least 95% of people who go see movies will dislike this movie.

  2. At least 95% of people who read books will dislike this movie.

  3. Most people who dislike this book will like this movie.

  4. Most people who like this book will dislike this movie.

Show Answer Correct Answer: D

Choice D is correct. The sample was selected from a group of people who indicated that they liked the book. It is inappropriate to generalize the result of the survey beyond the population from which the participants were selected. Choice D is the most appropriate inference from the survey results because it describes a conclusion about people who liked the book, and the results of the survey indicate that most people who like the book disliked the movie.

Choices A, B, and C are incorrect because none of these inferences can be drawn from the survey results. Choices A and B need not be true. The people surveyed all liked the book on which the movie was based, which is not necessarily true of all people who go see movies or all people who read books. Thus, the people surveyed are not representative of all people who go see movies or all people who read books. Therefore, the results of this survey cannot appropriately be extended to at least 95% of people who go see movies or to at least 95% of people who read books. Choice C need not be true because the sample includes only people who liked the book, and so the results do not extend to people who dislike the book.

Question 217 217 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?

  1. Mean

  2. Median

  3. Range

  4. Standard deviation

Show Answer Correct Answer: B

Choice B is correct. The median weight is found by ordering the horses’ weights from least to greatest and then determining the middle value from this list of weights. Decreasing the value for the horse with the lowest weight doesn’t affect the median since it’s still the lowest value.

Choice A is incorrect. The mean is calculated by finding the sum of all the weights of the horses and then dividing by the number of horses. Decreasing one of the weights would decrease the sum and therefore decrease the mean. Choice C is incorrect. Range is the difference between the highest and lowest weights, so decreasing the lowest weight would increase the range. Choice D is incorrect. Standard deviation is calculated based on the mean weight of the horses. Decreasing one of the weights decreases the mean and therefore would affect the standard deviation.

 

Question 218 218 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the relationship between two variables, x and y . A line of best fit is also shown.

  • The scatterplot has 6 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 3.4)
      • (8 comma 11)
      • (12 comma 14.8)

Which of the following equations best represents the line of best fit shown?

  1. y=x+3.4

  2. y=x-3.4

  3. y=-x+3.4

  4. y=-x-3.4

Show Answer Correct Answer: A

Choice A is correct. The line of best fit shown has a positive slope and intersects the y-axis at a positive y-value. The graph of an equation of the form y = m x + b , where m and b are constants, has a slope of m and intersects the y-axis at a y-value of b . Of the given choices, only y = x + 3.4 represents a line that has a positive slope, 1 , and intersects the y-axis at a positive y-value, 3.4 .

Choice B is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value.

Choice C is incorrect. This equation represents a line that has a negative slope, not a positive slope.

Choice D is incorrect. This equation represents a line that has a negative slope, not a positive slope, and intersects the y-axis at a negative y-value, not a positive y-value.

Question 219 219 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

For the values j and k , the ratio of j to k is 11 to 12 . If j is multiplied by 17 , what is k multiplied by in order to maintain the same ratio?

Show Answer Correct Answer: 17

The correct answer is 17 . If one value is multiplied by a number, then the other value must be multiplied by the same number in order to maintain the same ratio. It’s given that j is multiplied by 17 . Therefore, in order to maintain the same ratio, k must also be multiplied by 17 .

Question 220 220 of 368 selected Probability And Conditional Probability M

At a conference, there are a total of 275 attendees. Each attendee is assigned to either group A, group B, or group C. If one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is 0.44 and the probability of selecting an attendee who is assigned to group B is 0.24 . How many attendees are assigned to group C?

Show Answer Correct Answer: 88

The correct answer is 88 . It's given that there are a total of 275 attendees and each attendee is assigned to either group A, group B, or group C. It's also given that if one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is 0.44 and the probability of selecting an attendee who is assigned to group B is 0.24 . It follows that there are 0.44(275), or 121 , attendees who are assigned to group A and 0.24(275), or 66 , attendees who are assigned to group B. The number of attendees who are assigned to group C is the number of attendees who are not assigned to group A or group B. In other words, the number of attendees who are assigned to group C is the total number of attendees minus the number of attendees who are assigned to group A and group B. Therefore, the number of attendees who are assigned to group C is 275-121-66, or 88 .

Question 221 221 of 368 selected Two-Variable Data: Models And Scatterplots E

An airplane descends from an altitude of 9,500 feet to 5,000 feet at a constant rate of 400 feet per minute. What type of function best models the relationship between the descending airplane's altitude and time?

  1. Decreasing exponential

  2. Decreasing linear

  3. Increasing exponential

  4. Increasing linear

Show Answer Correct Answer: B

Choice B is correct. It′s given that the airplane descends at a constant rate of 400 feet per minute. Since the altitude decreases by a constant amount during each fixed time period, the relationship between the airplane′s altitude and time is linear. Since the airplane descends from an altitude of 9,500 feet to 5,000 feet, the airplane′s altitude is decreasing with time. Thus, the relationship is best modeled by a decreasing linear function.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 222 222 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

Marta has 7,500 pesos she will convert to US dollars using a currency exchange service. At this time, the currency exchange rate is 1 peso = 0.075 US dollars. The exchange service will charge Marta a 2% fee on the converted US dollar amount. How many US dollars will Marta receive from the currency exchange after the 2% fee is applied?

  1. $551.25

  2. $562.50

  3. $5,625.00

  4. $98,000.00

Show Answer Correct Answer: A

Choice A is correct. At the exchange rate of 1 peso = 0.075 US dollars, 7,500 pesos would be converted to 7,500 × 0.075 = $562.50. However, since Maria pays a 2% fee on the converted US dollar amount, she receives only (100 – 2)%, or 98%, of the converted US dollars, and 562.50 × 0.98 = $551.25.

Choice B is incorrect. This is the number of US dollars Maria would receive if the exchange service did not charge a 2% fee. Choice C is incorrect and may result from a decimal point error made when calculating the conversion to US dollars and from not assessing the 2% fee. Choice D is incorrect and may result from reversing the units of the exchange rate.

Question 223 223 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

71 , 72 , 73 , 76 , 77 , 79 , 83 , 87 , 93

What is the median of the data shown?

  1. 71

  2. 77

  3. 78

  4. 79

Show Answer Correct Answer: B

Choice B is correct. The median of a data set with an odd number of data values is defined as the middle value of the ordered list of values. The data set shown has nine values, so the median is the fifth value in the ordered list, which is 77 .

Choice A is incorrect. This is the minimum value of the data set, not the median.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the mean of the data set, not the median.

Question 224 224 of 368 selected Two-Variable Data: Models And Scatterplots H

The figure presents a scatterplot titled “Number of Beach Visitors versus Temperature.” The horizontal axis is labeled “Average temperature, in degrees Celsius,” and the numbers 25 through 35, in increments of 2, are indicated. The vertical axis is labeled “Number of people,” and the numbers 0 through 640, in increments of 80, are indicated. There are 11 data points in the scatterplot that begin near the bottom left portion of the coordinate plane and trend upward and to the right. The line of best fit for the data is also shown. The line of best fit passes through the points with coordinates 25 comma 80 and 32 comma 480.


Each dot in the scatterplot above represents the temperature and the number of people who visited a beach in Lagos, Nigeria, on one of eleven different days. The line of best fit for the data is also shown. The line of best fit for the data has a slope of approximately 57. According to this estimate, how many additional people per day are predicted to visit the beach for each 5°C increase in average temperature?

Show Answer

The correct answer is 285. The number of people predicted to visit the beach each day is represented by the y-values of the line of best fit, and the average temperature, in degrees Celsius (degrees Celsius), is represented by the x-values. Since the slope of the line of best fit is approximately 57, the y-value, or the number of people predicted to visit the beach each day, increases by 57 for every x-value increase of 1, or every 1 degree Celsius increase in average temperature. Therefore, an increase of 5 degrees Celsius in average temperature corresponds to a y-value increase of 57 times 5, equals 285 additional people per day predicted to visit the beach.

Question 225 225 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

Data set A consists of 9 data values, each of which is the integer 5.
Data set B consists of 10 data values, nine of which are the integer 5, and one of which is the integer 100.

Which of the following statements about the means and medians of data set A and data set B is true?

  1. Only the means are different.

  2. Only the medians are different.

  3. Both the means and the medians are different.

  4. Neither the means nor the medians are different.

Show Answer Correct Answer: A

Choice A is correct. The mean of a data set is the sum of the values divided by the number of values. The mean of data set A is the fraction 45 over 9, or 5. The mean of data set B is the fraction 145 over 10, or 14.5. Thus, the means are different. The median of a data set is the middle value when the values are ordered from least to greatest. The medians of data sets A and B are both 5. Therefore, the medians are the same, so only the means are different.

Choices B, C, and D are incorrect and may result from conceptual or calculation errors.

 

Question 226 226 of 368 selected Two-Variable Data: Models And Scatterplots E
The figure presents a scatterplot in the x y plane. The numbers 0 through 5, in increments of 1, are indicated along the x-axis. The numbers 0 through 6, in increments of 1, are indicated along the y-axis. There are 11 data points in the scatterplot. The data points begin on the y-axis at 6, and trend almost linearly downward and to the right. The data points end at the point with coordinates 5 comma 1.

Which of the following could be an equation for a line of best fit for the data in the scatterplot?

  1. y equals, negative x, plus 6

  2. y equals, negative x, minus 6

  3. y equals, 6 x, plus 1

  4. y equals, 6 x, minus 1

Show Answer Correct Answer: A

Choice A is correct. A line of best fit for the data in a scatterplot is a line that follows the trend of the data with approximately half the data points above and half the data points below the line. Based on the given data, a line of best fit will have a positive y-intercept on or near the point with coordinates 0 comma 6 and a negative slope. All of the choices are in slope-intercept form y equals, m x plus b, where m is the slope and b is the y-coordinate of the y-intercept. Only choice A is an equation of a line with a positive y-intercept at the point with coordinates 0 comma 6 and a negative slope, negative 1.

Choice B is incorrect. This equation is for a line that has a negative y-intercept, not a positive y-intercept. Choices C and D are incorrect and may result from one or more sign errors and from switching the values of the y-intercept and the slope in the equation.

 

Question 227 227 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E
Response Frequency
Once a week or more 3
Two or three times a month 16
About once a month 26
A few times a year 73
Almost never 53
Never 29
Total 200

The table gives the results of a survey of 200 people who were asked how often they see a movie in a theater. How many people responded either “never” or “almost never”?

  1. 24

  2. 53

  3. 82

  4. 118

Show Answer Correct Answer: C

Choice C is correct. The table gives the results of 200 people who were asked how often they see a movie in a theater. The table shows that 29 people responded “never” and 53 people responded “almost never.” Therefore, 29+53, or 82 , people responded either “never” or “almost never.”

Choice A is incorrect. This is the difference between the number of people who responded “almost never” and the number of people who responded “never.”

Choice B is incorrect. This is the number of people who responded “almost never” but doesn't include those who responded “never.”

Choice D is incorrect. This is the number of people who responded something other than “never” or “almost never,” rather than the number of people who responded either “never” or “almost never.”

Question 228 228 of 368 selected Percentages M

A customer’s monthly water bill was $75.74. Due to a rate increase, her monthly bill is now $79.86. To the nearest tenth of a percent, by what percent did the amount of the customer’s water bill increase?

  1. 4.1%

  2. 5.1%

  3. 5.2%

  4. 5.4%

Show Answer Correct Answer: D

Choice D is correct. To find the percent increase of the customer’s water bill, the absolute increase of the bill, in dollars, is divided by the original amount of the bill, and the result is multiplied by 100%, as follows: the fraction with numerator 79 point 8 6 minus 75 point 7 4, and denominator 75 point 7 4, is approximately equal to, 0 point 0 5 4;; 0 point 0 5 4 times 100 percent, equals 5 point 4 percent.

Choice A is incorrect. This choice is the difference 79 point 8 6, minus 75 point 7 4 rounded to the nearest tenth, which is the (absolute) increase of the bill’s amount, not its percent increase. Choice B is incorrect and may be the result of some calculation errors. Choice C is incorrect and is the result of dividing the difference between the two bill amounts by the new bill amount instead of the original bill amount.

Question 229 229 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

  • The data for the dot plot are as follows:
    • 22: 5 dots
    • 23: 4 dots
    • 24: 3 dots
    • 25: 2 dots
    • 26: 1 dot

The dot plot represents the 15 values in data set A. Data set B is created by adding 56 to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?

  1. The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A.

  2. The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A.

  3. The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.

  4. The median of data set B is greater than the median of data set A, and the range of data set B is greater than the range of data set A.

Show Answer Correct Answer: C

Choice C is correct. The median of a data set with an odd number of values, in ascending or descending order, is the middle value of the data set, and the range of a data set is the positive difference between the maximum and minimum values in the data set. Since the dot plot shown gives the values in data set A in ascending order and there are 15 values in the data set, the eighth value in data set A, 23 , is the median. The maximum value in data set A is 26 and the minimum value is 22 , so the range of data set A is 26-22, or 4 . It’s given that data set B is created by adding 56 to each of the values in data set A. Increasing each of the 15 values in data set A by 56 will also increase its median value by 56 making the median of data set B 79 . Increasing each value of data set A by 56 does not change the range, since the maximum value of data set B is 26+56, or 82 , and the minimum value is 22+56, or 78 , making the range of data set B 82-78, or 4 . Therefore, the median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 230 230 of 368 selected Two-Variable Data: Models And Scatterplots E
The figure presents the graph of a curve in a coordinate plane, titled “Braking Distance versus Speed.” The horizontal axis is labeled “Speed, in miles per hour,” and the numbers 0 through 80, in increments of 20, are indicated. The vertical axis is labeled “Braking distance, in feet,” and the numbers 0 through 600, in increments of 100, are indicated. Note that all of the following coordinate values are approximate. The graph starts at the origin, and moves steadily upward and to the right, passing through the point with coordinates 20 comma 50, the point with coordinates 40 comma 150, and the point with coordinates 60 comma 300. The graph then goes upward more rapidly as it moves to the right and ends approximately at the point with coordinates 80 comma 600.

The graph above shows the relationship between the speed of a particular car, in miles per hour, and its corresponding braking distance, in feet. Approximately how many feet greater will the car’s braking distance be when the car is traveling at 50 miles per hour than when the car is traveling at 30 miles per hour?

  1. 75

  2. 125

  3. 175

  4. 250

Show Answer Correct Answer: B

Choice B is correct. According to the graph, when the car is traveling at 50 miles per hour, the braking distance is approximately 225 feet, and when the car is traveling at 30 miles per hour, the braking distance is approximately 100 feet. The difference between these braking distances is 225 minus 100, or 125 feet.

Choice A is incorrect and may result from finding the braking distance for 20 miles per hour, the difference between the given speeds. Choice C is incorrect and may result from subtracting the speed from the braking distance at 50 miles per hour. Choice D is incorrect and may result from finding the difference in the braking distances at 60 and 20 miles per hour.

Question 231 231 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

Data set X: 5 , 9 , 9 , 13

Data set Y: 5 , 9 , 9 , 13 , 27

The lists give the values in data sets X and Y. Which statement correctly compares the mean of data set X and the mean of data set Y?

  1. The mean of data set X is greater than the mean of data set Y.

  2. The mean of data set X is less than the mean of data set Y.

  3. The means of data set X and data set Y are equal.

  4. There is not enough information to compare the means.

Show Answer Correct Answer: B

Choice B is correct. ​​The mean of a data set is the sum of the values in the data set divided by the number of values in the data set. It follows that the mean of data set X is 5+9+9+134, or 9 , and the mean of data set Y is 5+9+9+13+275, or 12.6 . Since 9 is less than 12.6 , the mean of data set X is less than the mean of data set Y.

Alternate approach: Data set Y consists of the 4 values in data set X and one additional value, 27 . Since the additional value, 27 , is larger than any value in data set X, the mean of data set X is less than the mean of data set Y.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 232 232 of 368 selected Two-Variable Data: Models And Scatterplots E

An orchard owner recorded the weight, in pounds, of all nectarines that grew on a dwarf nectarine tree during each growing season after the tree's transplantation. The scatterplot shows this weight, in pounds, for each growing season after the tree's transplantation.

  • The scatterplot has 8 data points.
  • The data points are in a linear pattern trending up from left to right.
  • The data points have the following coordinates:
    • (1 comma 0)
    • (2 comma 10)
    • (3 comma 21)
    • (4 comma 40)
    • (5 comma 46)
    • (6 comma 60)
    • (7 comma 76)
    • (8 comma 85)

What was the weight, to the nearest pound, of all nectarines that grew on the tree during the 4th growing season after the tree's transplantation?

Show Answer Correct Answer: 40

The correct answer is 40 . For each data point on the scatterplot, the x-value represents the growing season after transplantation and the y-value represents the weight, in pounds, of all nectarines that grew on the tree during the season. The scatterplot shows a data point at (4,40). It follows that during the 4 th growing season after the tree’s transplantation, 40 pounds of nectarines grew on the tree. 

Question 233 233 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

To study fluctuations in composition, samples of pumice were taken from 29 locations and cut in the shape of a cube. The length of the edge of one of these cubes is 3.000 centimeters. This cube has a density of 0.230 grams per cubic centimeter. What is the mass of this cube, in grams?

Show Answer Correct Answer: 6.21

The correct answer is 6.21 . It’s given that the samples of pumice were cut in the shape of a cube. It's also given that the length of the edge of one of these cubes is 3.000 centimeters. Therefore, the volume of this cube is (3.000 centimeters)3, or 27 cubic centimeters. Since the density of this cube is 0.230 grams per cubic centimeter, it follows that the mass of this cube is (0.230 grams1 cubic centimeter)(27 cubic centimeters), or 6.21 grams.

Question 234 234 of 368 selected Two-Variable Data: Models And Scatterplots M

In which of the following tables is the relationship between the values of x and their corresponding y-values nonlinear?

  1. The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 8. Column 2. x is 2. y is 11. Column 3. x is 3. y is 14. Column 4. x is 4. y is 17.

  2. The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 4. Column 2. x is 2. y is 8. Column 3. x is 3. y is 12. Column 4. x is 4. y is 16.

  3. The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 8. Column 2. x is 2. y is 13. Column 3. x is 3. y is 18. Column 4. x is 4. y is 23.

  4. The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 6. Column 2. x is 2. y is 12. Column 3. x is 3. y is 24. Column 4. x is 4. y is 48.

Show Answer Correct Answer: D

Choice D is correct. The relationship between the values of x and their corresponding y-values is nonlinear if the rate of change between these pairs of values isn’t constant. The table for choice D gives four pairs of values: the point with coordinates 1 comma 6 ,the point with coordinates 2 comma 12, the point with coordinates 3 comma 24 , and the point with coordinates 4 comma 48 . Finding the rate of change, or slope, between the point with coordinates 1 comma 6 and the point with coordinates 2 comma 12 by using the slope formula, the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction, yields the fraction with numerator 12 minus 6, and denominator 2 minus 1, end fraction, or 6. Finding the rate of change between the point with coordinates 2 comma 12 and the point with coordinates 3 comma 24 yields the fraction with numerator 24 minus 12, and denominator 3 minus 2, end fraction, or 12. Finding the rate of change between the point with coordinates 3 comma 24 and the point with coordinates 4 comma 48 yields the fraction with numerator 48 minus 24, and denominator 4 minus 3, end fraction, or 24. Since the rate of change isn’t constant for these pairs of values, this table shows a nonlinear relationship.

Choices A, B, and C are incorrect. The rate of change between the values of x and their corresponding y-values in each of these tables is constant, being 3, 4, and 5, respectively. Therefore, each of these tables shows a linear relationship.

Question 235 235 of 368 selected Probability And Conditional Probability E

There are n nonfiction books and 12 fiction books on a bookshelf. If one of these books is selected at random, what is the probability of selecting a nonfiction book, in terms of n ?

  1. the fraction n over 12

  2. the fraction n over n plus 12, end fraction

  3. the fraction 12 over n

  4. the fraction 12 over n plus 12, end fraction

Show Answer Correct Answer: B

Choice B is correct. Since there are n nonfiction and 12 fiction books on the bookshelf, n plus 12 represents the total number of books. If one of these books is selected at random, the probability of selecting a nonfiction book is equivalent to the number of nonfiction books divided by the total number of books. Therefore, the probability of selecting a nonfiction book, in terms of n, is the fraction with numerator n, and denominator n plus 12, end fraction.

Choice A is incorrect. This expression represents the number of nonfiction books divided by the number of fiction books. Choice C is incorrect. This expression represents the number of fiction books divided by the number of nonfiction books. Choice D is incorrect. This expression represents the probability of selecting a fiction book.

 

Question 236 236 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

  • The data for the 10 categories are as follows:
    • Group 1: 30
    • Group 2: 63
    • Group 3: 38
    • Group 4: 50
    • Group 5: 47
    • Group 6: 40
    • Group 7: 54
    • Group 8: 60
    • Group 9: 17
    • Group 10: 20

The bar graph shows the distribution of 419 cans collected by 10 different groups for a food drive. How many cans were collected by group 6 ?

Show Answer Correct Answer: 40

The correct answer is 40 . The height of each bar in the bar graph shown represents the number of cans collected by the group specified at the bottom of the bar. The bar for group 6 reaches a height of 40 . Therefore, group 6 collected 40 cans.

Question 237 237 of 368 selected Probability And Conditional Probability M

If 1,200 customers register for new accounts at a social media website every day, what fraction of the first 60,000 new accounts are registered in the first 5 days?

  1. one fifth

  2. one tenth

  3. one twelfth

  4. 1 over 50

Show Answer Correct Answer: B

Choice B is correct. If 1,200 customers register for new accounts every day, then (1,200)(5) = 6,000 customers registered for new accounts in the first 5 days. Therefore, of the first 60,000 new accounts that were registered, the fraction 6,000 over 60,000, or the fraction 1 over 10, were registered in the first 5 days.

Choice A is incorrect. The fraction one fifth represents the fraction of accounts registered in 1 of the first 5 days. Choice C is incorrect and may result from conceptual or computation errors. Choice D is incorrect. The fraction 1 over 50 represents the fraction of the first 60,000 accounts that were registered in 1 day.

 

Question 238 238 of 368 selected Percentages E

There are a total of 840 seats in a school auditorium. During an assembly, students occupied 50% of the seats in the auditorium. How many seats did the students occupy during this assembly?

  1. 25

  2. 50

  3. 420

  4. 790

Show Answer Correct Answer: C

Choice C is correct. It's given that during an assembly, students occupied 50% of the 840 seats in the school auditorium. Therefore, the number of seats that the students occupied during this assembly can be calculated by multiplying the number of seats in the school auditorium by 50100. Thus, the students occupied 840(50100), or 420 , seats during this assembly.

Choice A is incorrect. This is approximately 3%, not 50%, of 840 .

Choice B is incorrect. This is approximately 6%, not 50%, of 840 .

Choice D is incorrect. This is approximately 94%, not 50%, of 840 .

Question 239 239 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

How many tablespoons are equivalent to 14 teaspoons? (3 teaspoons=1 tablespoon)

Show Answer Correct Answer: 14/3, 4.666, 4.667

The correct answer is 143. It's given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 14 teaspoons is equivalent to (14 teaspoons)(1 tablespoon3 teaspoons), or 143 tablespoons. Note that 14/3, 4.666, and 4.667 are examples of ways to enter a correct answer.

Question 240 240 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A certain bird species can fly at an average speed of 16 meters per second when in continuous flight. At this rate, how many meters would this bird species fly in 4 seconds?

  1. 64

  2. 20

  3. 16

  4. 12

Show Answer Correct Answer: A

Choice A is correct. It's given that a certain bird species can fly at an average speed of 16 meters per second when in continuous flight. At this rate, in 4 seconds this bird species would fly (16 meterssecond)(4 seconds), or 64 meters.

Choice B is incorrect. This is the value of 16+4, not 16(4).

Choice C is incorrect. This is the distance the bird would fly in 1 second, not 4 seconds.

Choice D is incorrect. This is the value of 16-4, not 16(4).

Question 241 241 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

20181614121086420Number of volunteersABCD Gift
  • The Number of volunteers data for the 4 bars are as follows:
    • A: 14
    • B: 8
    • C: 18
    • D: 3

In April, there were 43 volunteers in a cleanup project. Each volunteer was asked to choose a small gift labeled A, B, C, or D. The bar graph shows the number of volunteers who chose each gift. How many volunteers chose gift C?

  1. 3

  2. 8

  3. 14

  4. 18

Show Answer Correct Answer: D

Choice D is correct. The height of each bar in the graph shown represents the number of volunteers who chose the gift labeled with the letter specified at the bottom of the bar. The bar for gift C has a height of 18 . Therefore, 18 volunteers chose gift C.

Choice A is incorrect. This is the number of volunteers who chose gift D, not gift C.

Choice B is incorrect. This is the number of volunteers who chose gift B, not gift C.

Choice C is incorrect. This is the number of volunteers who chose gift A, not gift C.

 

 

Question 242 242 of 368 selected Percentages M

The amount of Hanna's bill for a food order was $50. Hanna gave a tip of 20% of the amount of the bill. What is the amount, in dollars, of the tip Hanna gave?

Show Answer Correct Answer: 10

The correct answer is 10 . It’s given that the amount of Hanna's food order was $50 and that Hanna gave a tip of 20% of the amount of the bill. 20% of 50 can be calculated as (20100)(50), which yields 1000100, or 10 . Therefore, the amount, in dollars, of the tip Hanna gave is 10 .

Question 243 243 of 368 selected Two-Variable Data: Models And Scatterplots M

In the given scatterplot, a line of best fit for the data is shown.

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • The line of best fit passes through the following approximate coordinates:
      • (1 comma 3.3)
      • (3 comma 7.0)
      • (5 comma 10.8)

Which of the following is closest to the slope of the line of best fit shown?

  1. 0

  2. 1 2

  3. 1

  4. 2

Show Answer Correct Answer: D

Choice D is correct. A line in the xy-plane that passes through the points (x1,y1) and (x2,y2) has a slope of y2-y1x2-x1. The line of best fit shown passes approximately through the points (1,3.3) and (7,14.5). It follows that the slope of this best fit line is approximately 14.5-3.37-1, which is equivalent to 11.26, or approximately 1.87 . Therefore, of the given choices, 2 is closest to the slope of the line of best fit shown.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 244 244 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

If a is the mean and b is the median of nine consecutive integers, what is the value of the absolute value of, a, minus b, end absolute value ?

Show Answer

The correct answer is 0. Any nine consecutive integers can be written as k, k plus 1, k plus 2, k plus 3, k plus 4, k plus 5, k plus 6, k plus 7, k plus 8. The mean of the integers is their sum divided by 9: the fraction with numerator open parenthesis, k plus, k plus 1, plus, k plus 2, plus, dot dot dot, plus, k plus 8, close parenthesis, and denominator 9, equals, the fraction with numerator, open parenthesis, 9 k plus 36, close parenthesis, and denominator 9, which simplifies to k plus 4. So a, equals, k plus 4. Since there is an odd number of integers (nine), the median is the integer in the middle when all the integers are ordered from least to greatest: k plus 4. So b equals, k plus 4. Therefore, the absolute value of a, minus b, end absolute value, equals, the absolute value of, open parenthesis, k plus 4, close parenthesis, minus, open parenthesis, k plus 4, close parenthesis, end absolute value, which is 0.

Question 245 245 of 368 selected Percentages E

Isabel grows potatoes in her garden. This year, she harvested 760 potatoes and saved 10% of them to plant next year. How many of the harvested potatoes did Isabel save to plant next year?

  1. 66

  2. 76

  3. 84

  4. 86

Show Answer Correct Answer: B

Choice B is correct. The number of harvested potatoes Isabel saved to plant next year can be calculated by multiplying the total number of potatoes Isabel harvested, 760 , by the proportion of potatoes she saved. Since she saved 10% of the potatoes she harvested, the proportion of potatoes she saved is 10100, or 0.1 . Multiplying 760 by this proportion gives 760(0.1), or 76 , potatoes that she saved to plant next year.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 246 246 of 368 selected Two-Variable Data: Models And Scatterplots E

The line graph shows the estimated number of chipmunks in a state park on April 1 of each year from 1989 to 1999.

  • The line graph:
    • Begins at 1989, 38 chipmunks
    • Remains level to 1990, 38 chipmunks
    • Rises sharply to 1991, 98 chipmunks 
    • Rises gradually to 1992, 101 chipmunks
    • Falls sharply to 1993, 53 chipmunks
    • Rises sharply to 1994, 158 chipmunks 
    • Falls sharply to 1995, 48 chipmunks 
    • Rises sharply to 1996, 98 chipmunks 
    • Falls gradually to 1997, 93 chipmunks
    • Falls sharply to 1998, 53 chipmunks 
    • Rises sharply to 1999, 113 chipmunks

Based on the line graph, in which year was the estimated number of chipmunks in the state park the greatest?

  1. 1989

  2. 1994

  3. 1995

  4. 1998

Show Answer Correct Answer: B

Choice B is correct. For the given line graph, the estimated number of chipmunks is represented on the vertical axis. The greatest estimated number of chipmunks in the state park is indicated by the greatest height in the line graph. This height is achieved when the year is 1994.

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.

Question 247 247 of 368 selected Percentages H

According to the 2010 Census, the adult population aged 18 years or greater of the United States in 2010 was 234,564,071. In 2010, a survey was conducted among a randomly chosen sample of adults aged 18 years or greater in the United States about their preference to live in a warm climate or a cool climate. The table below displays a summary of the survey results.

Climate Preferences
 WarmCoolNo preferenceTotal
18–35 years old29516845508
36–50 years old24612341410
51–65 years old23811748403
Greater than 65 years old1377864279
Total9164861981,600
 

Which of the following is closest to the difference between the percentage of adults aged 18–50 years who responded “warm” and the percentage of adults aged 51 years or greater who responded “warm”?

  1. 4%

  2. 5%

  3. 10%

  4. 18%

Show Answer Correct Answer: A

Choice A is correct. The percentage of adults aged 18–50 who responded “warm” is the fraction with numerator 295 plus 246, and denominator 508 plus 410, end fraction, equals the fraction 541 over 918, or about 58.9%. The percentage of adults aged 51 years or greater who responded “warm” is the fraction with numerator 238 plus 137, and denominator 403 plus 279, end fraction, equals the fraction 375 over 682, or about 55.0%. The difference between 58.9% and 55.0% is 3.9%. Of the answer choices, 4% is closest to this number.

Choices B, C, and D are incorrect and may result from calculation errors.

Question 248 248 of 368 selected Percentages E

Lani spent 15% of her 8-hour workday in meetings. How many minutes of her workday did she spend in meetings?

  1. 1.2

  2. 15

  3. 48

  4. 72

Show Answer Correct Answer: D

Choice D is correct. There are 60 minutes in one hour, so an 8-hour workday has 60 times 8, equals 480 minutes. To calculate 15% of 480, multiply 0.15 by 480: 0 point 1 5 times 480, equals 72. Therefore, Lani spent 72 minutes of her workday in meetings.

Choice A is incorrect because 1.2 is 15% of 8, which gives the time Lani spent of her workday in meetings in hours, not minutes. Choices B and C are incorrect and may be the result of computation errors.

 

Question 249 249 of 368 selected Two-Variable Data: Models And Scatterplots E

The graph of function f is shown, where y=f(x).

  • The line slants gradually up from left to right.
  • The line passes through the following points:
    • (negative 6 comma negative StartFraction 16 Over 5 EndFraction)
    • (0 comma 0)
    • (6 comma StartFraction 16 Over 5 EndFraction)

Which of the following describes function f ?

  1. Increasing linear

  2. Decreasing linear

  3. Increasing exponential

  4. Decreasing exponential

Show Answer Correct Answer: A

Choice A is correct. The graph of function f shows that as x increases, f(x) also increases, which means f(x) is an increasing function. The graph of f is a line, which indicates a constant rate of change. A function that has a constant rate of change is a linear function. Therefore, function f can be described as increasing linear.

Choice B is incorrect. For a decreasing function, as x increases, f(x) decreases, rather than increases.

Choice C is incorrect. For a decreasing function, as x increases, f(x) decreases, rather than increases, and the graph of an exponential function isn't a line.

Choice D is incorrect. The graph of an exponential function isn't a line.

Question 250 250 of 368 selected Percentages H

The number a is 70% less than the positive number b . The number c is 60% greater than a . The number c is how many times b ?

Show Answer Correct Answer: .48, 12/25

The correct answer is .48. It's given that the number a is 70% less than the positive number b . Therefore, a=(1-70100)b, which is equivalent to a=(1-0.70)b, or a=0.30b. It's also given that the number c is 60% greater than a . Therefore, c=(1+60100)a, which is equivalent to c=(1+0.60)a, or c=1.60a. Since a = 0.30 b , substituting 0.30 b for a in the equation c = 1.60 a yields c=1.60(0.30b), or c=0.48b. Thus, c is 0.48 times b . Note that .48 and 12/25 are examples of ways to enter a correct answer.

Question 251 251 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A special camera is used for underwater ocean research. The camera is at a depth of 39 fathoms. What is the camera's depth in feet? (1 fathom=6 feet)

  1. 234

  2. 117

  3. 45

  4. 7

Show Answer Correct Answer: A

Choice A is correct. It’s given that a special camera is used for underwater ocean research, and this camera is at a depth of 39 fathoms. It's also given that 1 fathom is equal to 6 feet. Thus, 39 fathoms is equivalent to (39 fathoms)(6 feet1 fathom), or 234 feet. Therefore, the camera's depth, in feet, is 234 .

Choice B is incorrect. This is the camera's depth, in feet, if the camera is at a depth of 19.5 fathoms.

Choice C is incorrect. This is the camera's depth, in feet, if the camera is at a depth of 7.5 fathoms.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 252 252 of 368 selected Probability And Conditional Probability E

Each of 157 gemstones can be classified as one of three classifications, as shown in the frequency table.

Classification Frequency
color X 119
color Y 3
color Z 35

If one of the gemstones is selected at random, what is the probability of selecting a gemstone of color Y?

  1. 3157

  2. 35157

  3. 119157

  4. 154157

Show Answer Correct Answer: A

Choice A is correct. If one of the gemstones is selected at random, the probability of selecting a gemstone of color Y is equal to the number of gemstones of color Y divided by the total number of gemstones. According to the table, there are 3 gemstones of color Y, and it's given that the total number of gemstones is 157 . Therefore, if one of the gemstones is selected at random, the probability of selecting a gemstone of color Y is 3 157 .

Choice B is incorrect. This is the probability of selecting a gemstone of color Z.

Choice C is incorrect. This is the probability of selecting a gemstone of color X.

Choice D is incorrect. This is the probability of selecting a gemstone that's not of color Y.

Question 253 253 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

Five Smallest Countries in 2016

Country Land area
 (square kilometers)
Monaco 2.0
Nauru 21
San Marino 61
Tuvalu 26
Vatican City 0.44

The table above shows the land area, in square kilometers, of the five smallest countries of the world in 2016. Based on the table, what is the mean land area of the 5 smallest countries in 2016, to the nearest square kilometer?

  1. 20

  2. 22

  3. 61

  4. 110

Show Answer Correct Answer: B

Choice B is correct. The mean land area of these 5 countries is equal to the sum of the land areas of these countries, or 2 point 0, plus 21, plus 61, plus 26, plus 0 point 4 4, divided by the number of countries in the table, 5, or the fraction with numerator 2 point 0, plus 21, plus 61, plus 26, plus 0 point 4 4, and denominator 5. Combining like terms in the numerator yields 110 point 4 4 over 5, which simplifies to 22.088 square kilometers. This value, when rounded to the nearest square kilometer, is 22.

Choice A is incorrect and may result from a calculation error. Choice C is incorrect. This is the greatest land area of the 5 countries in the table. Choice D is incorrect. This is the sum of the land areas of the 5 countries in the table, rounded to the nearest square kilometer.

 

Question 254 254 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments H

Near the end of a US cable news show, the host invited viewers to respond to a poll on the show’s website that asked, “Do you support the new federal policy discussed during the show?” At the end of the show, the host reported that 28% responded “Yes,” and 70% responded “No.” Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?

  1. The percentages do not add up to 100%, so any possible conclusions from the poll are invalid.

  2. Those who responded to the poll were not a random sample of the population of the United States.

  3. There were not 50% “Yes” responses and 50% “No” responses.

  4. The show did not allow viewers enough time to respond to the poll.

Show Answer Correct Answer: B

Choice B is correct. In order for the poll results from a sample of a population to represent the entire population, the sample must be representative of the population. A sample that is randomly selected from a population is more likely than a sample of the type described to represent the population. In this case, the people who responded were people with access to cable television and websites, which aren’t accessible to the entire population. Moreover, the people who responded also chose to watch the show and respond to the poll. The people who made these choices aren’t representative of the entire population of the United States because they were not a random sample of the population of the United States.

Choices A, C, and D are incorrect because they present reasons unrelated to whether the sample is representative of the population of the United States.

 

Question 255 255 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

A triathlon is a multisport race consisting of three different legs. A triathlon participant completed the cycling leg with an average speed of 19.700 miles per hour. What was the average speed, in yards per hour, of the participant during the cycling leg? (1 mile=1,760 yards)

Show Answer Correct Answer: 34672

The correct answer is 34,672 . It's given that 1 mile=1,760 yards. It follows that an average speed of 19.700 miles per hour is equivalent to (19.700 miles1 hour)(1,760 yards1 mile), or 34,672 yards per hour.

Question 256 256 of 368 selected Probability And Conditional Probability M
United States Presidents
from 1789 to 2015
AgesNumber
40–442
45–497
50–5413
55–5911
60–647
65–693

The table above gives the number of United States presidents from 1789 to 2015 whose age at the time they first took office is within the interval listed. Of those presidents who were at least 50 years old when they first took office, what fraction were at least 60 years old?

  1. 10 over 43

  2. 10 over 34

  3. 10 over 24

  4. 25 over 34

Show Answer Correct Answer: B

Choice B is correct. The sample space is restricted to the presidents who were at least 50 years old when they first took office. Therefore, the sum of the values in the final four rows of the table, 13 plus 11, plus 7, plus 3, equals 34, is the total number of presidents in the sample space. The number of presidents who were at least 60 years old is the sum of the values in the final two rows of the table: 7 plus 3, equals 10. Thus, the fraction of the 34 presidents who were at least 50 years old when they first took office who were at least 60 years old is 10 over 34.

Choice A is incorrect. This is the fraction of all presidents in the table who were at least 60 years old when they first took office. Choice C is incorrect and may result from treating the number of presidents who were between 50 and 59 years old when they first took office, instead of the number of presidents who were at least 50 years old, as the sample space. Choice D is incorrect and may result from a calculation error.

 

Question 257 257 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

Objects R and S each travel at a constant speed. The speed of object R is half the speed of object S. Object R travels a distance of 4 x inches in y seconds. Which expression represents the time, in seconds, it takes object S to travel a distance of 24 x inches?

  1. 12 y

  2. 3 y

  3. 16 y

  4. 6 y

Show Answer Correct Answer: B

Choice B is correct. It's given that object R travels a distance of 4 x inches in y seconds. This speed can be written as 4x inchesy seconds. It's given that the speed of object R is half the speed of object S. It follows that the speed of object S is twice the speed of object R, which is 2(4x inchesy seconds), or 8x inchesy seconds. Let n represent the time, in seconds, it takes object S to travel a distance of 24 x inches. The value of n can be found by solving the equation 8x inchesy seconds=24x inchesn seconds, which can be written as 8 x y = 24 x n . Multiplying each side of this equation by n y yields 8xn=24xy. Dividing each side of this equation by 8 x yields n = 3 y . Therefore, the expression 3 y represents the time, in seconds, it takes object S to travel a distance of 24 x inches.

Choice A is incorrect. This expression represents the time, in seconds, it would take object S to travel a distance of 24 x inches if the speed of object R were twice, not half, the speed of object S.

Choice C is incorrect. This expression represents the time, in seconds, it takes object S to travel a distance of 128 x inches, not 24 x inches.

Choice D is incorrect. This expression represents the time, in seconds, it takes object R, not object S, to travel a distance of 24 x inches.

Question 258 258 of 368 selected Probability And Conditional Probability H

The table below shows the distribution of US states according to whether they have a state-level sales tax and a state-level income tax.

2013 State-Level Taxes
  State sales tax No state sales tax
State income tax 39 4
No state income tax 6 1

 

To the nearest tenth of a percent, what percent of states with a state-level sales tax do not have a state-level income tax?

  1. 6.0%

  2. 12.0%

  3. 13.3%

  4. 14.0%

Show Answer Correct Answer: C

Choice C is correct. The sum of the number of states with a state-level sales tax is 39 plus 6, equals 45. Of these states, 6 don’t have a state-level income tax. Therefore, 6 over 45, equals 0 point 1 3 3 3 dot dot dot, or about 13.3%, of states with a state-level sales tax don’t have a state-level income tax.


Choice A is incorrect. This is the number of states that have a state-level sales tax and no state-level income tax. Choice B is incorrect. This is the percent of states that have a state-level sales tax and no state-level income tax. Choice D is incorrect. This is the percent of states that have no state-level income tax.

 

Question 259 259 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

An object's speed is 64 yards per second. What is the object's speed, in feet per second? (1 yard=3 feet)

  1. 61

  2. 67

  3. 94

  4. 192

Show Answer Correct Answer: D

Choice D is correct. Since 1 yard is equal to 3 feet, 64 yards is equal to 64 yards(3 feet1 yard), or 192 feet. It follows that 64 yards per second is equivalent to 192 feet per second. Therefore, the object's speed is 192 feet per second.

Choice A is incorrect. A speed of 61 feet per second is equivalent to 613, not 64 , yards per second.

Choice B is incorrect. A speed of 67 feet per second is equivalent to 673, not 64 , yards per second.

Choice C is incorrect. A speed of 94 feet per second is equivalent to 943, not 64 , yards per second.

Question 260 260 of 368 selected Percentages H

The result of increasing the quantity x by 1,800% is 684 . What is the value of x ?

  1. 12,996

  2. 12,312

  3. 38

  4. 36

Show Answer Correct Answer: D

Choice D is correct. It’s given that the result of increasing the quantity x by 1,800% is 684 . It follows that x+(1,800100)x=684, which is equivalent to x+18x=684, or 19x=684. Dividing each side of this equation by 19 yields x = 36 . Therefore, the value of x is 36 .

Choice A is incorrect. The result of increasing the quantity 12,996 by 1,800% is 246,924, not 684 .

Choice B is incorrect. The result of increasing the quantity 12,312 by 1,800% is 233,928, not 684 .

Choice C is incorrect. The result of increasing the quantity 38 by 1,800% is 722 , not 684 .

Question 261 261 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

Tilly earns p dollars for every w hours of work. Which expression represents the amount of money, in dollars, Tilly earns for 39 w hours of work?

  1. 39 p

  2. p39

  3. p + 39

  4. p - 39

Show Answer Correct Answer: A

Choice A is correct. It’s given that Tilly earns p dollars for every w hours of work. This can be represented by the proportion pw. The amount of money, x , Tilly earns for 39 w hours of work can be found by setting up the proportion pw=x39w. This can be rewritten as 39pw=xw. Dividing both sides by w results in x = 39 p

Choice B is incorrect. This is the amount of money Tilly earns in dollars per hour, not the amount of money Tilly earns for 39 w hours of work.

Choice C is incorrect. This is the amount of money Tilly earns for w hours of work plus 39 , not the amount of money Tilly earns for 39 w hours of work.

Choice D is incorrect. This is the amount of money Tilly earns for w hours of work minus 39 , not the amount of money Tilly earns for 39 w hours of work.

Question 262 262 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

The total area of a coastal city is 92.1 square miles, of which 11.3 square miles is water. If the city had a population of 621,000 people in the year 2010, which of the following is closest to the population density, in people per square mile of land area, of the city at that time?

  1. 6,740

  2. 7,690

  3. 55,000

  4. 76,000

Show Answer Correct Answer: B

Choice B is correct. The land area of the coastal city can be found by subtracting the area of the water from the total area of the coastal city; that is, 92 point 1, minus 11 point 3, equals 80 point 8 square miles. The population density is the population divided by the land area, or the fraction 621,000 over 80 point 8, end fraction, equals 7,686, which is closest to 7,690 people per square mile.

Choice A is incorrect and may be the result of dividing the population by the total area, instead of the land area. Choice C is incorrect and may be the result of dividing the population by the area of water. Choice D is incorrect and may be the result of making a computational error with the decimal place.

Question 263 263 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

The bar graph shows the number of each type of monkey in a sanctuary. 

1211109876543210Number of monkeysmandrillbaboonpygmy marmosetbonnet macaquevervet Type of monkey
  • The Number of monkeys data for the 5 bars are as follows:
    • mandrill: 5
    • baboon: 7
    • pygmy marmoset: 8
    • bonnet macaque: 9
    • vervet: 11

How many more vervets are in this sanctuary than mandrills?

  1. 11

  2. 6

  3. 5

  4. 3

Show Answer Correct Answer: B

Choice B is correct. It's given that the bar graph shows the number of each type of monkey in a sanctuary. The bar representing the number of mandrills has a height of 5 ; therefore, there are 5 mandrills in the sanctuary. The bar representing vervets has a height of 11 ; therefore, there are 11 vervets in the sanctuary. Therefore, there are 11-5, or 6 , more vervets in this sanctuary than mandrills.

Choice A is incorrect. This is the number of vervets in the sanctuary.

Choice C is incorrect. This is the number of mandrills in the sanctuary. 

Choice D is incorrect and may result from conceptual or calculation errors.

Question 264 264 of 368 selected Probability And Conditional Probability E

-11 , -9 , 26

A data set of three numbers is shown. If a number from this data set is selected at random, what is the probability of selecting a positive number?

  1. 0

  2. 1 3

  3. 2 3

  4. 1

Show Answer Correct Answer: B

Choice B is correct. The probability of selecting a positive number is the number of positive numbers in the data set divided by the total number of numbers in the data set. There is 1 positive number in this data set. There are 3 total numbers in this data set. Thus, if a number from this data set is selected at random, the probability of selecting a positive number is 1 3 .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the probability of selecting a negative number from this data set.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 265 265 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

d equals, 55 t

The equation above can be used to calculate the distance d, in miles, traveled by a car moving at a speed of 55 miles per hour over a period of t hours. For any positive constant k, the distance the car would have traveled after 9 k hours is how many times the distance the car would have traveled after 3 k hours?

  1. 3

  2. 6

  3. 3k

  4. 6 k

Show Answer Correct Answer: A

Choice A is correct. Since the distance is equal to the amount of time multiplied by a constant, the given equation d equals 55 t represents a proportional relationship between distance and time in this situation. Since 9 k equals, 3 times 3 k, the time when t equals 9 k hours is 3 times the time when t equals 3 k hours. Therefore, the distance traveled after 9 k hours is 3 times the distance after 3 k hours.

Choices B and D are incorrect and may result from interpreting the proportional relationship between time and distance as additive rather than multiplicative. Choice C is incorrect and may result from an arithmetic error.

 

Question 266 266 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

A distance of 354 furlongs is equivalent to how many feet? (1 furlong=220 yards and 1 yard=3 feet)

  1. 306

  2. 402

  3. 25,960

  4. 233,640

Show Answer Correct Answer: D

Choice D is correct. It's given that 1 furlong=220 yards and 1 yard=3 feet. It follows that a distance of 354 furlongs is equivalent to (354 furlongs)(220 yards1 furlong)(3 feet1 yard), or 233,640 feet.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 267 267 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

One side of a flat board has an area of 874 square inches. If a pressure of 19 pounds per square inch of area is exerted on this side of the board, what is the total force, in pounds, exerted on this side of the board?

Show Answer Correct Answer: 16606

The correct answer is 16,606 . It's given that one side of a flat board has an area of 874 square inches. If a pressure of 19 pounds per square inch of area is exerted on this side of the board, the total force exerted on this side of the board is (874 square inches)(19 pounds1 square inch), or 16,606 pounds.

Question 268 268 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

Data set A consists of the heights of 75 objects and has a mean of 25 meters. Data set B consists of the heights of 50 objects and has a mean of 65 meters. Data set C consists of the heights of the 125 objects from data sets A and B. What is the mean, in meters, of data set C?

Show Answer Correct Answer: 41

The correct answer is 41 . The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It’s given that data set A consists of the heights of 75 objects and has a mean of 25 meters. This can be represented by the equation x 75 = 25 , where x represents the sum of the heights of the objects, in meters, in data set A. Multiplying both sides of this equation by 75 yields x=75(25), or x = 1,875 meters. Therefore, the sum of the heights of the objects in data set A is 1,875 meters. It’s also given that data set B consists of the heights of 50 objects and has a mean of 65 meters. This can be represented by the equation y 50 = 65 , where y represents the sum of the heights of the objects, in meters, in data set B. Multiplying both sides of this equation by 50 yields y=50(65), or y = 3,250 meters. Therefore, the sum of the heights of the objects in data set B is 3,250 meters. Since it’s given that data set C consists of the heights of the 125 objects from data sets A and B, it follows that the mean of data set C is the sum of the heights of the objects, in meters, in data sets A and B divided by the number of objects represented in data sets A and B, or 1,875+3,250125, which is equivalent to 41 meters. Therefore, the mean, in meters, of data set C is 41 .

Question 269 269 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

Data set F consists of 55 integers between 170 and 290 . Data set G consists of all the integers in data set F as well as the integer 10 . Which of the following must be less for data set F than for data set G?

  1. The mean
  2. The median
  1. I only

  2. II only

  3. I and II

  4. Neither I nor II

Show Answer Correct Answer: D

Choice D is correct. It's given that data set F consists of 55 integers between 170 and 290 and data set G consists of all the integers in data set F as well as the integer 10 . Since the integer 10 is less than all the integers in data set F, the mean of data set G must be less than the mean of data set F. Thus, the mean of data set F isn't less than the mean of data set G. When a data set is in ascending order, the median is between the two middle values when there is an even number of values and the median is the middle value when there is an odd number of values. It follows that the median of data set F is either greater than or equal to the median of data set G. Therefore, the median of data set F isn't less than the median of data set G. Thus, neither the mean nor the median must be less for data set F than for data set G.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 270 270 of 368 selected Inference From Sample Statistics And Margin Of Error M

Based on a random sample from a population, a researcher estimated that the mean value of a certain variable for the population is 20.5 , with an associated margin of error of 1 . Which of the following is the most appropriate conclusion?

  1. It is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5 .

  2. It is not possible that the mean value of the variable for the population is less than 19.5 or greater than 21.5 .

  3. Every value of the variable in the population is between 19.5 and 21.5 .

  4. The mean value of the variable for the population is 20.5 .

Show Answer Correct Answer: A

Choice A is correct. It's given that based on a random sample from a population, the estimated mean value for a certain variable for the population is 20.5, with an associated margin of error of 1 . This means that it is plausible that the actual mean value of the variable for the population is between 20.5-1 and 20.5+1. Therefore, the most appropriate conclusion is that it is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5.

Choice B is incorrect. The estimated mean value and associated margin of error describe only plausible values, not all the possible values, for the actual mean value of the variable, so this is not an appropriate conclusion.

Choice C is incorrect. The estimated mean value and associated margin of error describe only plausible values for the actual mean value of the variable, not all the possible values of the variable, so this is not an appropriate conclusion.

Choice D is incorrect. Since 20.5 is the estimated mean value of the variable based on a random sample, the actual mean value of the variable may not be exactly 20.5. Therefore, this is not an appropriate conclusion.

Question 271 271 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

  • From left to right the values of the vertical bars in the box plot are as follows:
    • First vertical bar: 2
    • Second vertical bar: 4
    • Third vertical bar: 5
    • Fourth vertical bar: 7
    • Fifth vertical bar: 8

 

The box plot summarizes 15 data values. What is the median of this data set?

  1. 2

  2. 3

  3. 5

  4. 8

Show Answer Correct Answer: C

Choice C is correct. The median of a data set represented in a box plot is given by the vertical line within the box. In the given box plot, the vertical line within the box occurs at 5 . Therefore, the median of this data set is 5 .

Choice A is incorrect. This is the minimum value of the data set.

Choice B is incorrect and may result from conceptual errors.

Choice D is incorrect. This is the maximum value of the data set.

Question 272 272 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

Data set A consists of the heights of 75 buildings and has a mean of 32 meters. Data set B consists of the heights of 50 buildings and has a mean of 62 meters. Data set C consists of the heights of the 125 buildings from data sets A and B. What is the mean, in meters, of data set C?

Show Answer Correct Answer: 44

The correct answer is 44 . The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It's given that data set A consists of the heights of 75 buildings and has a mean of 32 meters. This can be represented by the equation x 75 = 32 , where x represents the sum of the heights of the buildings, in meters, in data set A. Multiplying both sides of this equation by 75 yields x=75(32), or x = 2,400 meters. Therefore, the sum of the heights of the buildings in data set A is 2,400 meters. It's also given that data set B consists of the heights of 50 buildings and has a mean of 62 meters. This can be represented by the equation y 50 = 62 , where y represents the sum of the heights of the buildings, in meters, in data set B. Multiplying both sides of this equation by 50 yields y=50(62), or y = 3,100 meters. Therefore, the sum of the heights of the buildings in data set B is 3,100 meters. Since it's given that data set C consists of the heights of the 125 buildings from data sets A and B, it follows that the mean of data set C is the sum of the heights of the buildings, in meters, in data sets A and B divided by the number of buildings represented in data sets A and B, or 2,400+3,100125, which is equivalent to 44 meters. Therefore, the mean, in meters, of data set C is 44 .

Question 273 273 of 368 selected Percentages H

After 20% of the original number of marbles in a group were removed from the group, 360 marbles remained in the group. How many marbles were removed from the group?

  1. 72

  2. 90

  3. 450

  4. 1,800

Show Answer Correct Answer: B

Choice B is correct. It's given that 20% of the original number of marbles were removed from the group. Let x represent the original number of marbles in the group. It follows that 20100x, or 0.20x, marbles were removed from the group. Therefore, x-0.20x marbles remained in the group. It's also given that 360 marbles remained in the group. Thus, x-0.20x=360, or 0.80x=360. Dividing both sides of this equation by 0.80 yields x = 450 . Substituting 450 for x in the expression 0.20x yields 0.20(450), or 90 . Therefore, 90 marbles were removed from the group.

Choice A is incorrect. This is 20% of the remaining number of marbles.

Choice C is incorrect. This is the original number of marbles, not the number of marbles that were removed.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 274 274 of 368 selected Percentages H

The number a is 110% greater than the number b . The number b is 90% less than 47 . What is the value of a ?

Show Answer Correct Answer: 9.87, 987/100

The correct answer is 9.87 . It’s given that the number a is 110% greater than the number b . It follows that a=(1+110100)b, or a = 2.1 b . It’s also given that the number b is 90% less than 47 . It follows that b=(1-90100)(47), or b=0.1(47), which yields b = 4.7 . Substituting 4.7 for b in the equation a = 2.1 b yields a=2.1(4.7), which is equivalent to a = 9.87 . Therefore, the value of a is 9.87 .

Question 275 275 of 368 selected Percentages E

There are 170 blocks in a container. Of these blocks, 10% are green. How many blocks in the container are green?

Show Answer Correct Answer: 17

The correct answer is 17 . It's given that there are 170 blocks in a container, and of these blocks, 10% are green. Since 10% can be rewritten as 10100, or 0.1, the number of green blocks in the container is 0.1(170), or 17 .

Question 276 276 of 368 selected Percentages E
Call Ratings
1 Star 2 Stars 3 Stars 4 Stars Total
Employee A 16 49 72 8 145
Employee B

4

10 22 34 70
Employee C 8 56 45 16 125
Employee D 22 42 84 12 160
Total 50 157 223 70 500

A supervisor at a call center reviewed 500 calls taken by four employees and rated the employees’ performance on each call on a scale from 1 star to 4 stars. The ratings for each employee are shown in the table above. According to the table, to the nearest whole percent, what percent of Employee A’s calls received a rating of 1 star?

  1. 3%

  2. 11%

  3. 16%

  4. 32%

Show Answer Correct Answer: B

Choice B is correct. The percent of Employee A’s calls that received a rating of 1 star is the number of Employee A’s 1-star calls divided by the total number of Employee A’s calls. This quotient, 16 over 145, is approximately equal to 0 point 1 1 0 3, or 11 point 0 3 percent. To the nearest whole percent, this is 11%.

Choice A is incorrect. This is the percent of all calls taken by Employee A that received a rating of 1 star. Choice C is incorrect and may result from a conceptual error. For example, 16 is the number, not the percent, of calls taken by Employee A that received a rating of 1 star. Choice D is incorrect. This is the percent of all calls that received a rating of 1 star that were taken by Employee A.

Question 277 277 of 368 selected Evaluating Statistical Claims: Observational Studies And Experiments H

To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true?

  1. The mean number of children per household in the community is 2.4.

  2. A determination about the mean number of children per household in the community should not be made because the sample size is too small.

  3. The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.

  4. The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community.

Show Answer Correct Answer: C

Choice C is correct. In order to use a sample mean to estimate the mean for a population, the sample must be representative of the population (for example, a simple random sample). In this case, Tabitha surveyed 20 families in a playground. Families in the playground are more likely to have children than other households in the community. Therefore, the sample isn’t representative of the population. Hence, the sampling method is flawed and may produce a biased estimate.

Choices A and D are incorrect because they incorrectly assume the sampling method is unbiased. Choice B is incorrect because a sample of size 20 could be large enough to make an estimate if the sample had been representative of all the families in the community.

Question 278 278 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A participant in a bicycle race completes the race with an average speed of 24,816 yards per hour. What is this average speed, in miles per hour? (1 mile=1,760 yards)

Show Answer Correct Answer: 14.1

The correct answer is 14.1 . It’s given that a participant completes the bicycle race with an average speed of 24,816 yards per hour and 1 mile=1,760 yards. It follows that this average speed is equivalent to (24,816 yards1 hour)(1 mile1,760 yards), which yields 14.1 miles1 hour, or 14.1 miles per hour.

Question 279 279 of 368 selected Percentages H

140 is p% greater than 10 . What is the value of p ?

  1. 1,400

  2. 1,300

  3. 140

  4. 130

Show Answer Correct Answer: B

Choice B is correct. It's given that 140 is p% greater than 10 . It follows that 140=10+(p100)10, which is equivalent to 140=10+10100p, or 140=10+0.1p. Subtracting 10 from each side of this equation yields 130=0.1p. Dividing each side of this equation by 0.1 yields 1,300=p, or p=1,300.

Choice A is incorrect. This would be the value of p if 140 were p% of 10 , not p% greater than 10 .

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 280 280 of 368 selected Two-Variable Data: Models And Scatterplots E

The figure presents a scatterplot titled “Number of Beach Visitors versus Temperature.” The horizontal axis is labeled “Average temperature, in degrees Celsius,” and the numbers 25 through 35, in increments of 2, are indicated. The vertical axis is labeled “Number of people,” and the numbers 0 through 640, in increments of 80, are indicated. There are 11 data points in the scatterplot that begin near the bottom left portion of the coordinate plane and trend upward and to the right. The line of best fit for the data is also shown. The line of best fit passes through the points with coordinates 25 comma 80 and 32 comma 480.

Each dot in the scatterplot above represents the temperature and the number of people who visited a beach in Lagos, Nigeria, on one of eleven different days. The line of best fit for the data is also shown. According to the line of best fit, what is the number of people, rounded to the nearest 10, predicted to visit this beach on a day with an average temperature of 32°C?

Show Answer

The correct answer is 480. An average temperature of 32 degrees Celsius corresponds to the value 32 on the x-axis. On the line of best fit, an x-value of 32 corresponds to a y-value of 480. The values on the y-axis correspond to the number of people predicted to visit this beach. Therefore, 480 people are predicted to visit this beach on a day with an average temperature of 32 degrees Celsius.

Question 281 281 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

For an electric field passing through a flat surface perpendicular to it, the electric flux of the electric field through the surface is the product of the electric field’s strength and the area of the surface. A certain flat surface consists of two adjacent squares, where the side length, in meters, of the larger square is 3 times the side length, in meters, of the smaller square. An electric field with strength 29.00 volts per meter passes uniformly through this surface, which is perpendicular to the electric field. If the total electric flux of the electric field through this surface is 4,640 volts·meters, what is the electric flux, in volts·meters, of the electric field through the larger square?

Show Answer Correct Answer: 4176

The correct answer is 4,176 . It’s given that the side length of the larger square is 3 times the side length of the smaller square. This means that the area of the larger square is 32, or 9 , times the area of the smaller square. If the area of the smaller square is represented by x , then the area of the larger square can be represented by 9 x . Therefore, the flat surface of the two adjacent squares has a total area of x+9x, or 10 x . It’s given that an electric field with strength 29.00 volts per meter passes uniformly through this surface and the total electric flux of the electric field through this surface is 4,640 volts·meters. Since it's given that the electric flux is the product of the electric field’s strength and the area of the surface, the equation 29.00(10x)=4,640, or 290x=4,640, can be used to represent this situation. Dividing each side of this equation by 290 yields x = 16 . Substituting 16 for x in the expression for the area of the larger square, 9 x , yields 9(16), or 144 , square meters. Since the area of the larger square is 144 square meters, the electric flux, in volts·meters, of the electric field through the larger square can be determined by multiplying the area of the larger square by the strength of the electric field. Thus, the electric flux is (144 square meters)(29.00 voltsmeter), or 4,176 volts·meters.

Question 282 282 of 368 selected Two-Variable Data: Models And Scatterplots H

The scatterplot below shows the amount of electric energy generated, in millions of megawatt-hours, by nuclear sources over a 10‑year period.

The figure presents a scatterplot in the xy-plane titled “Electric Energy Generated by Nuclear Sources.” The x-axis is labeled “Time,” in years, and the numbers zero through 12, in increments of 2, are indicated. The y-axis is labeled “Energy,” in million megawatt-hours, and the numbers 700 through 820, in increments of 20, are indicated. There are 10 data points scattered in the form of a curve. The first data point begins approximately at the point with coordinates 1 comma 764. The points follow a path varying upward and downward and to the right, until reaching the point with coordinates of approximately 8 comma 806. The points then move downward and to the right, ending at the point with coordinates of approximately 10 comma 768. 
The data represented by the points are as follows. Note that all values are approximate.
Point 1: 1 year, 764 million mega-watt hours. 
Point 2: 2 years, 788 million mega-watt hours.
Point 3: 3 years, 781 million mega-watt hours.
Point 4: 4 years, 785 million mega-watt hours.
Point 5: 5 years, 804 million mega-watt hours.
Point 6: 6 years, 803 million mega-watt hours.
Point 7: 7 years, 796 million mega-watt hours.
Point 8: 8 years, 806 million mega-watt hours.
Point 9: 9 years, 790 million mega-watt hours.
Point 10: 10 years, 768 million mega-watt hours.

 

Of the following equations, which best models the data in the scatterplot?

  1. y equals 1 point six seven four x squared, plus 19 point seven six x, minus 745 point seven three

  2. y equals negative 1 point six seven four x squared, minus 19 point seven six x, minus 745 point seven three

  3. y equals 1 point six seven four x squared, plus 19 point seven six x, plus 745 point seven three

  4. y equals negative 1 point six seven four  x squared, plus 19 point seven six x, plus 745 point seven three

Show Answer Correct Answer: D

Choice D is correct. The data in the scatterplot roughly fall in the shape of a downward-opening parabola; therefore, the coefficient for the x squared term must be negative. Based on the location of the data points, the y-intercept of the parabola should be somewhere between 740 and 760. Therefore, of the equations given, the best model is y equals, negative 1 point 6 7 4, x squared, plus 19 point 7 6 x, plus 745 point 7 3.

Choices A and C are incorrect. The positive coefficient of the x squared term means that these equations each define upward-opening parabolas, whereas a parabola that fits the data in the scatterplot must open downward. Choice B is incorrect because it defines a parabola with a y-intercept that has a negative y-coordinate, whereas a parabola that fits the data in the scatterplot must have a y-intercept with a positive y-coordinate.

 

Question 283 283 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

A landscaper uses a hose that puts 88 x ounces of water in a bucket in 5 y minutes. Which expression represents the number of ounces of water the hose puts in the bucket in 9 y minutes at this rate?

  1. 9 x 440

  2. 440 x 9

  3. 5 x 792

  4. 792 x 5

Show Answer Correct Answer: D

Choice D is correct. It’s given that a hose puts 88 x ounces of water in a bucket in 5 y minutes. Therefore, the rate at which the hose puts water in the bucket, in ounces per minute, can be represented by the expression 88x5y. Let w represent the number of ounces of water the hose puts in the bucket in 9 y minutes at this rate. It follows that the rate at which the hose puts water in the bucket, in ounces per minute, can be represented by the expression w9y. The expressions 88x5y and w9y represent the same rate, so it follows that 88x5y=w9y. Multiplying both sides of this equation by 9 y yields 792xy5y=w, or 792 x 5 = w . Therefore, the number of ounces of water the hose puts in the bucket in 9 y minutes can be represented by the expression 792 x 5 .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 284 284 of 368 selected Two-Variable Data: Models And Scatterplots M
The figure presents a scatterplot in the first quadrant of the x y plane. The numbers 0 through 10, in increments of 2, are indicated on the x axis. The numbers 0 through 30, in increments of 5, are indicated on the y axis. There are 8 data points in the scatterplot. The data points begin at the point with approximate coordinates 1 comma 4, and trend upward and to the right until they end at the point with approximate coordinates 8 comma 26.

Which of the following could be the equation for a line of best fit for the data shown in the scatterplot above?

  1. y equals, 3 x plus 0 point 8

  2. y equals, 0 point 8 x, plus 3

  3. y equals, negative 0 point 8 x, plus 3

  4. y equals, negative 3 x plus 0 point 8

Show Answer Correct Answer: A

Choice A is correct. The data show a strong linear relationship between x and y. The line of best fit for a set of data is a linear equation that minimizes the distances from the data points to the line. An equation for the line of best fit can be written in slope-intercept form, y equals, m x plus b, where m is the slope of the graph of the line and b is the y-coordinate of the y-intercept of the graph. Since, for the data shown, the y-values increase as the x-values increase, the slope of a line of best fit must be positive. The data shown lie almost in a line, so the slope can be roughly estimated using the formula for slope, m equals, the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction. The leftmost and rightmost data points have coordinates of about 1 comma 4 and 8 comma 26, so the slope is approximately the fraction with numerator 26 minus 4, and denominator 8 minus 1, end fraction, equals the fraction 22 over 7, which is a little greater than 3. Extension of the line to the left would intersect the y-axis at about the point with coordinates 0 comma 1. Only choice A represents a line with a slope close to 3 and a y-intercept close to the point with coordinates 0 comma 1.

Choice B is incorrect and may result from switching the slope and y-intercept. The line with a y-intercept of 0 comma 3 and a slope of 0.8 is farther from the data points than the line with a slope of 3 and a y-intercept of 0 comma 0 point 8. Choices C and D are incorrect. They represent lines with negative slopes, not positive slopes.

 

Question 285 285 of 368 selected Percentages E

There were approximately 113,000 occupational therapy jobs in the United States in 2012. The Bureau of Labor Statistics has projected that this number will increase by 29% from 2012 to 2022. Of the following, which is closest to the number of occupational therapy jobs the bureau has projected for the United States in 2022?

  1. 115,900

  2. 116,300

  3. 142,000

  4. 145,800

Show Answer Correct Answer: D

Choice D is correct. The decimal equivalent of 29% is 0.29. It’s given that the 113,000 occupational therapy jobs in the United States in 2012 are projected to increase by 29% by 2022. Increasing 113,000 by 29% can be expressed as 113,000 times, open parenthesis, 1 plus 0 point 2 9, close parenthesis, or 113,000 times 1 point 2 9. Evaluating this expression yields 145,770. The closest number is 145,800 in choice D.

Choice A is incorrect and may result from increasing 113,000 by 2,900 instead of by 29%. Choice B is incorrect and may result from increasing 113,000 by 2.9% instead of by 29%. Choice C is incorrect and may result from increasing 113,000 by 29,000 instead of by 29%.

 

Question 286 286 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

  • The data for the 10 categories are as follows:
    • Group 1: 30
    • Group 2: 62
    • Group 3: 36
    • Group 4: 50
    • Group 5: 46
    • Group 6: 40
    • Group 7: 54
    • Group 8: 60
    • Group 9: 16
    • Group 10: 20

The bar graph shows the distribution of 414 books collected by 10 different groups for a book drive. How many books were collected by group 1 ?

Show Answer Correct Answer: 30

The correct answer is 30 . The height of each bar in the bar graph shown represents the number of books collected by the group specified at the bottom of the bar. The bar for group 1 reaches a height of 30 . Therefore, group 1 collected 30 books.

Question 287 287 of 368 selected Percentages E

A waiter receives tips from each customer. On average, the tip is 15% of the customer’s bill. At this rate, which of the following is closest to the tip the waiter can expect when a customer has a bill that is $78.20?

  1. $8.00

  2. $10.00

  3. $12.00

  4. $14.00

Show Answer Correct Answer: C

Choice C is correct. If the bill is $78.20, 15% of the bill can be found by multiplying 78.20 by the decimal conversion of 15%, 78.20 × 0.15 = $11.73. The exact amount $11.73 is closest in value to $12.00.

Choices A, B, and D are incorrect and may be the result of errors when calculating 15% of the total $78.20.

Question 288 288 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

An object travels at a constant speed of 6 centimeters per second. At this speed, what is the time, in seconds, that it would take for the object to travel 24 centimeters?

Show Answer Correct Answer: 4

The correct answer is 4 . It’s given that the object travels at a constant speed of 6 centimeters per second. The speed of the object can be written as 6 centimeters1 second. Let x represent the time, in seconds, it would take for the object to travel 24 centimeters. The value of x can be calculated by solving the equation 6 centimeters1 second=24 centimetersx seconds, which can be written as 61=24x, or 6=24x. Multiplying each side of this equation by x yields 6 x = 24 . Dividing each side of this equation by 6 yields x = 4 . Therefore, it would take the object 4 seconds to travel 24 centimeters.

Question 289 289 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the temperature y , in °F, recorded by a meteorologist at various times x , in days since June 1

  • The scatterplot has 7 data points.
  • The data points are in a linear pattern trending approximately horizontally.
  • The data points have the following coordinates:
    • (1 comma 69)
    • (2 comma 60)
    • (3 comma 73)
    • (4 comma 67)
    • (5 comma 64)
    • (6 comma 62)
    • (7 comma 65)

During which of the following time periods did the greatest increase in recorded temperature take place?

  1. From x=6 to x=7

  2. From x=5 to x=6

  3. From x=2 to x=3

  4. From x=1 to x=2

Show Answer Correct Answer: C

Choice C is correct. The scatterplot shows that there was an increase in recorded temperature from x=2 to x=3 and from x=6 to x=7. When x=2, the recorded temperature was approximately 60°F and when x=3, the recorded temperature was greater than 70°F. This means that the increase in recorded temperature from x=2 to x=3 was greater than (70-60)°F, or 10°F. When x=6, the recorded temperature was greater than 60°F and when x=7, the recorded temperature was less than 70°F. This means that the increase in recorded temperature from x=6 to x=7 was less than (70-60)°F, or 10°F. It follows that the greatest increase in recorded temperature took place from x=2 to x=3.

Choice A is incorrect. The increase in recorded temperature from x=6 to x=7 was less than the increase in recorded temperature from x=2 to x=3.

Choice B is incorrect. From x=5 to x=6, a decrease, not an increase, in recorded temperature took place.

Choice D is incorrect. From x=1 to x=2, a decrease, not an increase, in recorded temperature took place.

Question 290 290 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

Makayla is planning an event in a 5,400-square-foot room. If there should be at least 8 square feet per person, what is the maximum number of people that could attend this event?

  1. 588

  2. 675

  3. 15,274

  4. 43,200

Show Answer Correct Answer: B

Choice B is correct. It’s given that the event will be in a 5,400-square-foot room and that there should be at least 8 square feet per person. The maximum number of people that could attend the event can be found by dividing the total square feet in the room by the minimum number of square feet needed per person, which gives the fraction 5,400 over 8, equals 675.

Choices A and C are incorrect and may result from conceptual or computational errors. Choice D is incorrect and may result from multiplying, rather than dividing, 5,400 by 8.

Question 291 291 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

A product costs 11.00 dollars per pound. What is the cost, in dollars, for 6 pounds of the product?

Show Answer Correct Answer: 66

The correct answer is 66 . It’s given that a product costs 11.00 dollars per pound. Therefore, the cost for 6 pounds of the product is (11.00 dollars1 pound)(6 pounds), which is equivalent to 66.00, or 66 , dollars.

Question 292 292 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

  • The data for the 5 categories are as follows: 
    • 1: More than halfway above 25 students
    • 2: Less than halfway above 30 students
    • 3: More than halfway above 35 students
    • 4: About halfway above 40 students
    • 5: About halfway above 45 students

A group of students voted on five after-school activities. The bar graph shows the number of students who voted for each of the five activities. How many students chose activity 3 ?

  1. 25

  2. 39

  3. 48

  4. 50

Show Answer Correct Answer: B

Choice B is correct. The height of each bar in the bar graph given represents the number of students that voted for the activity specified at the bottom of the bar. The bar for activity 3 has a height that is between 35 and 40 . In other words, the number of students that chose activity 3 is between 35 students and 40 students. Of the given choices, 39 is the only value between 35 and 40 . Therefore, 39 students chose activity 3 .

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect. This is the number of students that chose activity 5 , not activity 3 .

Choice D is incorrect and may result from conceptual errors.

Question 293 293 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H
The figure presents a 2-column table, with 7 rows of data, titled “Percent of Residents Who Earned a Bachelor’s Degree or Higher.” The heading for the first column is “State,” and the heading for the second column is “Percent of residents.” The 7 rows of data are as follows.

Row 1. State A; 21 point 9 percent.
Row 2. State B; 27 point 9 percent.
Row 3. State C; 25 point 9 percent.
Row 4. State D; 19 point 5 percent.
Row 5. State E; 30 point 1 percent.
Row 6. State F; 36 point 4 percent.
Row 7. State G; 35 point 5 percent.

A survey was given to residents of all 50 states asking if they had earned a bachelor’s degree or higher. The results from 7 of the states are given in the table above. The median percent of residents who earned a bachelor’s degree or higher for all 50 states was 26.95%. What is the difference between the median percent of residents who earned a bachelor’s degree or higher for these 7 states and the median for all 50 states?

  1. 0.05%

  2. 0.95%

  3. 1.22%

  4. 7.45%

Show Answer Correct Answer: B

Choice B is correct. The median of a set of numbers is the middle value of the set values when ordered from least to greatest. If the percents in the table are ordered from least to greatest, the middle value is 27.9%. The difference between 27.9% and 26.95% is 0.95%.

Choice A is incorrect and may be the result of calculation errors or not finding the median of the data in the table correctly. Choice C is incorrect and may be the result of finding the mean instead of the median. Choice D is incorrect and may be the result of using the middle value of the unordered list.

Question 294 294 of 368 selected Percentages H

The number w is 110% greater than the number z . The number z is 55% less than 50 . What is the value of w ?

Show Answer Correct Answer: 189/4, 47.25

The correct answer is 47.25 . It’s given that the number w is 110% greater than the number z . It follows that w=(1+110100)z, or w=2.1z. It’s also given that the number z is 55% less than 50 . It follows that z=(1-55100)(50), or z=0.45(50), which yields z=22.5. Substituting 22.5 for z in the equation w=2.1z yields w=2.1(22.5), which is equivalent to w = 47.25 . Therefore, the value of w is 47.25 . Note that 47.25 and 189/4 are examples of ways to enter a correct answer.

Question 295 295 of 368 selected Percentages M

432 is 96 % of what number?

Show Answer Correct Answer: 450

The correct answer is 450 . Let x represent the number that 432 is 96% of. This can be written as (96100)x=432, or 0.96x=432. Dividing both sides of this equation by 0.96 yields x = 450 . Therefore, 432 is 96% of 450 .

Question 296 296 of 368 selected Two-Variable Data: Models And Scatterplots E

A study was done to determine a new car’s stopping distance when it was traveling at different speeds. The study was done on a dry road with good surface conditions. The results are shown below, along with the graph of a quadratic function that models the data.

The figure presents a graph in the x y-plane titled “Vehicle Stopping Distance.” The x-axis is labeled “Speed, in miles per hour,” and the numbers zero through 80, in increments of 20, are indicated. The y-axis is labeled “Stopping Distance, in feet” and the numbers zero through 350, in increments of 50, are indicated. In the graph, there are six data points indicated from left to right with each point strictly to the right and above the preceding point. From left to right, the approximate coordinates of the six points are as follows. 

Point 1: 20 comma 40.
Point 2: 30 comma 75.
Point 3: 40 comma 120.
Point 4: 50 comma 185.
Point 5: 60 comma 240.
Point 6: 70 comma 315.

A quadratic curve is shown on the graph. The curve begins at point 1 and curves upward and to the right, passing through point 2 and point 3. It then passes slightly below point 4 and slightly above point 5, ending at point 6.

According to the model, which of the following is the best estimate for the stopping distance, in feet, if the vehicle was traveling 55 miles per hour?

  1. 25
  2. 30
  3. 210

  4. 250

Show Answer Correct Answer: C

Correct Answer Rationale
Choice C is correct. According to the model, the stopping distance, in feet, of a vehicle traveling 55 miles per hour is about 200 feet. Of the choices given, the best estimate of the stopping distance for a car traveling 55 miles per hour is 210 feet.

Incorrect Answer Rationale
Choices A, B, and D are incorrect and may be the result of incorrectly reading the given quadratic model. The corresponding x-values to the y-values of 25 and 30 are not part of the model. The corresponding x-value to a y-value of 250 is approximately 60 mph, not 55 mph.

Question 297 297 of 368 selected Two-Variable Data: Models And Scatterplots E

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending down from left to right.
  • Select data points have the following approximate coordinates:
    • (0.8 comma 8.9)
    • (2.8 comma 5.1)
    • (4.1 comma 2.9)

Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?

  1. y = - 1.9 x - 10.1

  2. y = - 1.9 x + 10.1

  3. y = 1.9 x - 10.1

  4. y = 1.9 x + 10.1

Show Answer Correct Answer: B

Choice B is correct. The equation representing a linear model can be written in the form y=a+bx, or y=bx+a, where b is the slope of the graph of the model and (0,a) is the y-intercept of the graph of the model. The scatterplot shows that as the x-values of the data points increase, the y-values of the data points decrease, which means the graph of an appropriate linear model has a negative slope. Therefore, b<0. The scatterplot also shows that the data points are close to the y-axis at a positive value of y . Therefore, the y-intercept of the graph of an appropriate linear model has a positive y-coordinate, which means a>0. Of the given choices, only choice B, y=-1.9x+10.1, has a negative value for b , the slope, and a positive value for a , the y-coordinate of the y-intercept. 

Choice A is incorrect. The graph of this model has a y-intercept with a negative y-coordinate, not a positive y-coordinate.

Choice C is incorrect. The graph of this model has a positive slope, not a negative slope, and a y-intercept with a negative y-coordinate, not a positive y-coordinate.

Choice D is incorrect. The graph of this model has a positive slope, not a negative slope.

Question 298 298 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

A fish hatchery has three tanks for holding fish before they are introduced into the wild. Ten fish weighing less than 5 ounces are placed in tank A. Eleven fish weighing at least 5 ounces but no more than 13 ounces are placed in tank B. Twelve fish weighing more than 13 ounces are placed in tank C. Which of the following could be the median of the weights, in ounces, of these 33 fish?

  1. 4.5

  2. 8

  3. 13.5

  4. 15

Show Answer Correct Answer: B

Choice B is correct. The median of a set of numbers is the middle number when the values in the set are ordered from least to greatest. There are 33 fish, so in an ordered list of the weights, the 17th value would be the median weight. The 10 fish in tank A weigh the least, and these 10 weights would be the first 10 values on the ordered list. The 11 fish in tank B have the next set of higher weights, and so would be the 11th through 21st weights in the ordered list, which includes the median weight as the 17th value. The fish in tank B weigh at least 5 ounces but no more than 13 ounces; of the given choices, only 8 ounces falls within this range of values.

Choice A is incorrect. It’s given that tank A has ten fish weighing less than 5 ounces. Since there are more than ten fish in tanks B and C combined, the median weight cannot be less than 5 ounces. Choice C and D are incorrect. It’s given that tank C has twelve fish weighing more than 13 ounces. There are more than twelve fish in tanks A and B combined, so the median weight can’t be more than 13 ounces.

 

Question 299 299 of 368 selected Inference From Sample Statistics And Margin Of Error H

In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

  1. 16,200

  2. 23,400

  3. 30,600

  4. 46,800

Show Answer Correct Answer: C

Choice C is correct. It is given that 34.6% of 26 students in Mr. Camp’s class reported that they had at least two siblings. Since 34.6% of 26 is 8.996, there must have been 9 students in the class who reported having at least two siblings and 17 students who reported that they had fewer than two siblings. It is also given that the average eighth-grade class size in the state is 26 and that Mr. Camp’s class is representative of all eighth-grade classes in the state. This means that in each eighth-grade class in the state there are about 17 students who have fewer than two siblings. Therefore, the best estimate of the number of eighth-grade students in the state who have fewer than two siblings is 17 × (number of eighth-grade classes in the state), or 17 times 1,800, equals 30,600.

Choice A is incorrect because 16,200 is the best estimate for the number of eighth-grade students in the state who have at least, not fewer than, two siblings. Choice B is incorrect because 23,400 is half of the estimated total number of eighth-grade students in the state; however, since the students in Mr. Camp’s class are representative of students in the eighth-grade classes in the state and more than half of the students in Mr. Camp’s class have fewer than two siblings, more than half of the students in each eighth-grade class in the state have fewer than two siblings, too. Choice D is incorrect because 46,800 is the estimated total number of eighth-grade students in the state.

Question 300 300 of 368 selected Two-Variable Data: Models And Scatterplots M

In the given scatterplot, a line of best fit for the data is shown.

  • The scatterplot has 5 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 0.2)
      • (5 comma 9.3)

Which of the following is closest to the slope of the line of best fit shown?

  1. 0.2

  2. 0.7

  3. 1.8

  4. 2.6

Show Answer Correct Answer: C

Choice C is correct. A line in the xy-plane that passes through points (x1,y1) and (x2,y2) has a slope of y2-y1x2-x1. The line of best fit shown passes approximately through the points (0,0.2) and (5,9.3). It follows that the slope of this line is approximately 9.3-0.25-0, which is equivalent to 9.15, or 1.82. Therefore, of the given choices, 1.8 is closest to the slope of the line of best fit shown.

Choice A is incorrect. This value is closest to the y-coordinate of the y-intercept of the line of best fit shown.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 301 301 of 368 selected Percentages H

The number of zebras in a population in 2018 was 1.27 times the number of zebras in this population in 2014. If the number of zebras in this population in 2014 is p% of the number of zebras in this population in 2018, what is the value of p , to the nearest whole number?

Show Answer Correct Answer: 79

The correct answer is 79 . Let x represent the number of zebras in the population in 2014 and let y represent the number of zebras in the population in 2018 . It’s given that the number of zebras in this population in 2018 was 1.27 times the number of zebras in this population in 2014 . It follows that the equation y = 1.27 x represents this situation. Dividing both sides of this equation by 1.27 yields y1.27=x, or (11.27)y=x. Therefore, the number of zebras in this population in 2014 is 11.27 times the number of zebras in this population in 2018 . If the number of zebras in this population in 2014 is p% of the number of zebras in this population in 2018 , then x=p100y. It follows that 11.27=p100, or 1001.27=p, which means p is approximately equal to 78.74 . Therefore, the value of p , to the nearest whole number, is 79 .

Question 302 302 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

The figure presents a bar graph titled “Results of Five Quality Control Trials.” The horizontal axis is labeled “Trial,” and the following five letters are indicated along the axis: A, B, C, D, and E. Each letter has a vertical bar. The vertical axis is labeled “Number of defective light bulbs,” and the numbers 0 through 8, in increments of 1, are indicated. The data represented by each of the 5 bars are as follows.  Trial A, 4 light bulbs. Trial B, 7 light bulbs. Trial C, 1 light bulb. Trial D, 3 light bulbs. Trial E, 6 light bulbs.

For quality control, a company that manufactures lightbulbs conducted five different trials. In each trial, 500 different lightbulbs were tested. The bar graph above shows the number of defective lightbulbs found in each trial. What is the mean number of defective lightbulbs for the five trials?

  1. 4.0

  2. 4.2

  3. 4.6

  4. 5.0

Show Answer Correct Answer: B

Choice B is correct. The numbers of defective lightbulbs found for the five trials are 4, 7, 1, 3, and 6, respectively. The mean is therefore the fraction with numerator 4, plus 7, plus 1, plus 3, plus 6, and denominator 5, equals 4 point 2.

Choice A is incorrect. This is the median number of defective lightbulbs for the five trials. Choice C is incorrect and may result from an arithmetic error. Choice D is incorrect and may result from mistaking the number of trials for the number of defective lightbulbs.

Question 303 303 of 368 selected Percentages M

What number is 40 % greater than 115 ?

Show Answer Correct Answer: 161

The correct answer is 161 . For a number to be 40% greater than 115 , it follows that the number is (100% of 115)+(40% of 115), which can be written as 100100(115)+40100(115). This expression is equivalent to 1(115)+0.4(115), or 1.4(115), which is equal to 161 . Therefore, 161 is 40% greater than 115 .

Question 304 304 of 368 selected Percentages M

13 is p% of 25 . What is the value of p ?

Show Answer Correct Answer: 52

The correct answer is 52 . It's given that 13 is p% of 25 . It follows that 13 25 = p 100 . Multiplying both sides of this equation by 100 gives 52 = p . Therefore, the value of p is 52 .

Question 305 305 of 368 selected Percentages E

During a sale, the original prices of all the items in a clothing store have been reduced by 20%. What is the sale price of a jacket with an original price of $50 ?

  1. $12

  2. $30

  3. $36

  4. $40

Show Answer Correct Answer: D

Choice D is correct. It’s given that the original price of the jacket has been reduced by 20%. Multiplying the original price, $50, by 20% gives the amount, in dollars, that the price of the jacket is reduced by: 50 times point 2 0, equals 10. Subtracting this value from the original price results in the sale price of the jacket: 50 dollars minus 10 dollars, or $40.

Choices A, B, and C are incorrect and may result from a conceptual or calculation error.

 

Question 306 306 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

A competition consisted of four different events. One participant completed the first event with an average speed of 20.300 miles per hour. What was this average speed, in yards per hour? (1 mile=1,760 yards)

Show Answer Correct Answer: 35728

The correct answer is 35,728 . It's given that 1 mile=1,760 yards. It follows that an average speed of 20.300 miles per hour is equivalent to (20.300 miles1 hour)(1,760 yards1 mile), or 35,728 yards per hour.

Question 307 307 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread M

A list consists of 5 numbers: 2, 10, 3, 7, 6

The mean of the list of numbers above is what fraction of the sum of the five numbers?

Show Answer

The correct answer is one fifth. The mean of the list of numbers is found by dividing the sum of the numbers by the number of values in the list. Since there are 5 numbers in the list, the mean is one fifth of the sum of the numbers. Note that 1/5 and .2 are examples of ways to enter a correct answer.

Question 308 308 of 368 selected Percentages M

There are 450 tiles in a box. Of these tiles, 6% are black. How many black tiles are in the box?

Show Answer Correct Answer: 27

The correct answer is 27 . It’s given that 6% of the 450 tiles in a box are black. Therefore, the number of black tiles in the box can be calculated by multiplying the number of tiles in the box by 6100, which is equivalent to 450(6100), or 27 .

Question 309 309 of 368 selected Two-Variable Data: Models And Scatterplots E

The figure presents a scatterplot titled “Temperature and Elevation.” The horizontal axis is labeled “Elevation, in feet,” and the numbers 6,000 through 9,000, in increments of 500, are indicated. The vertical axis is labeled “Temperature, in degrees Fahrenheit,” and the integers 37 through 45 are indicated. There are 8 data points. The data points begin a little below, and to the right of the top of the vertical axis, then trend downward and to the right. A line of best fit is drawn. The data represented by the 8 data points are as follows. Note that all values are approximate. Point 1. 6,350 feet, 42 point 9 degrees Fahrenheit. Point 2. 6,750 feet, 43 point 8 degrees Fahrenheit. Point 3. 6,750 feet, 42 degrees Fahrenheit. Point 4. 7,500 feet, 42 point 2 degrees Fahrenheit. Point 5. 8,000 feet, 40 point 5 degrees Fahrenheit. Point 6. 8,000 feet, 40 degrees Fahrenheit. Point 7. 8,800 feet, 38 point 6 degrees Fahrenheit. Point 8. 8,800 feet, 37 point 6 degrees Fahrenheit. The line of best fit passes through the data point representing 7,500 feet comma 41 point 1 degrees Fahrenheit, and the data point representing 8,500 feet comma 39 degrees Fahrenheit

The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. Which of the following statements best describes the association between the elevation and the temperature of locations in the Lake Tahoe Basin?

  1. As the elevation increases, the temperature tends to increase.

  2. As the elevation increases, the temperature tends to decrease.

  3. As the elevation decreases, the temperature tends to decrease.

  4. There is no association between the elevation and the temperature.

Show Answer Correct Answer: B

Choice B is correct. The association between the elevation and the temperature of locations in the Lake Tahoe Basin can be described by looking at the direction of the line of best fit. The line of best fit slopes downward, which corresponds to the temperature decreasing as the elevation increases.

Choices A and C are incorrect. Both of these choices would be represented by a line of best fit that slopes from the lower left to the upper right of the graph, which isn’t what’s shown on the graph. Choice D is incorrect. This choice would be represented by a line of best fit that is horizontal or has a slope very close to 0. This is not what’s shown on the graph.

Question 310 310 of 368 selected Two-Variable Data: Models And Scatterplots E

The table shows selected values from function f .

x f(x)
-1 16
0 17
1 18
2 19

Which of the following is the best description of function f ?

  1. Decreasing linear

  2. Increasing linear

  3. Decreasing exponential

  4. Increasing exponential

Show Answer Correct Answer: B

Choice B is correct. The given values show that as x increases, f(x) also increases, which means that f is an increasing function. Furthermore, f(x) increases at a constant rate of 1 for each increase of x by 1 . A function with a constant rate of change is linear. Thus, the function f can be described as an increasing linear function.

Choice A is incorrect. For a decreasing linear function, as x increases, f(x) decreases rather than increases.

Choice C is incorrect. For a decreasing exponential function, for each increase of x by 1 , f(x) decreases by a fixed percentage rather than increases at a constant rate.

Choice D is incorrect. For an increasing exponential function, for each increase of x by 1 , f(x) increases by a fixed percentage rather than at a constant rate.

Question 311 311 of 368 selected Inference From Sample Statistics And Margin Of Error E

Scott selected 20 employees at random from all 400 employees at a company. He found that 16 of the employees in this sample are enrolled in exactly three professional development courses this year. Based on Scott’s findings, which of the following is the best estimate of the number of employees at the company who are enrolled in exactly three professional development courses this year?

  1. 4

  2. 320

  3. 380

  4. 384

Show Answer Correct Answer: B

Choice B is correct. It’s given that from the sample of 20 employees at the company, 16 of the employees are enrolled in exactly three professional development courses this year. Since (1620) is equal to 0.80, or 80100, it follows that 80% of the employees in the sample are enrolled in exactly three professional development courses this year. Therefore, the best estimate for the percentage of employees at the company who are enrolled in exactly three professional development courses this year is 80%. It’s given that there are a total of 400 employees at the company. Therefore, the best estimate of the number of employees at the company who are enrolled in exactly three professional development courses this year is (80100)(400), or 320 .

Choice A is incorrect. This is the number of employees from the sample who aren't enrolled in exactly three professional development courses this year.

Choice C is incorrect. This is the number of employees who weren't selected for the sample. 

Choice D is incorrect and may result from conceptual or calculation errors.

Question 312 312 of 368 selected Percentages H

A gift shop buys souvenirs at a wholesale price of 7.00 dollars each and resells them each at a retail price that is 290% of the wholesale price. At the end of the season, any remaining souvenirs are marked at a discounted price that is 80% off the retail price. What is the discounted price of each remaining souvenir, in dollars?

Show Answer Correct Answer: 203/50, 4.06

The correct answer is 4.06 . It's given that the retail price is 290% of the wholesale price of $7.00. Thus, the retail price is $7.00(290100), which is equivalent to $7.00(2.9), or $20.30. It's also given that the discounted price is 80% off the retail price. Thus, the discounted price is $20.30(1-80100), which is equivalent to $20.30(0.20), or $4.06.

Question 313 313 of 368 selected Two-Variable Data: Models And Scatterplots H
The figure presents a scatterplot titled “Size and Sale Price of Houses in Town H.” The x axis is labeled “Size, in thousands of square feet,” and the numbers 0 through 3, in increments of 1, are indicated. The y axis is labeled “Sale price, in thousands of dollars,” and the numbers 0 through 400, in increments of 50, are indicated. 

There are 25 data points on the scatterplot. The data points begin in the middle left part of the graph, at the point with coordinates zero point 9 comma one hundred ninety. They trend upward and to the right in clusters, ending at the point with coordinates 2.55 comma 350.

A line of best fit for the data is not shown in the graph. However, it appears that if a line of best fit were drawn, it would pass through the point with coordinates zero comma one hundred and the point with coordinates 2 point 5 comma three hundred fifty.

The scatterplot above shows the size x and the sale price y of 25 houses for sale in Town H. Which of the following could be an equation for a line of best fit for the data?

  1. y equals, 200 x plus 100

  2. y equals, 100 x plus 100

  3. y equals, 50 x plus 100

  4. y equals, 100 x

Show Answer Correct Answer: B

Choice B is correct. From the shape of the cluster of points, the line of best fit should pass roughly through the points with coordinates 1 comma 200 and 2 point 5 comma 350. Therefore, these two points can be used to find an approximate equation for the line of best fit. The slope of this line of best fit is therefore the fraction with numerator y sub 2, minus y sub 1, and denominator x sub 2, minus x sub 1, end fraction, equals, the fraction with numerator 350 minus 200, and denominator 2 point 5 minus 1, end fraction, or 100. The equation for the line of best fit, in slope-intercept form, is y equals, 100 x plus b for some value of b. Using the point with coordinates 1 comma 200, 1 can be substituted for x and 200 can be substituted for y: 200 equals, 100 times 1, plus b, or b equals 100. Substituting this value into the slope-intercept form of the equation gives y equals, 100 x plus 100.

Choice A is incorrect. The line defined by y equals, 200 x plus 100 passes through the points with coordinates 1 comma 300 and 2 comma 500, both of which are well above the cluster of points, so it cannot be a line of best fit. Choice C is incorrect. The line defined by y equals, 50 x plus 100 passes through the points with coordinates 1 comma 150 and 2 comma 200, both of which lie at the bottom of the cluster of points, so it cannot be a line of best fit. Choice D is incorrect and may result from correctly calculating the slope of a line of best fit but incorrectly assuming the y-intercept is at the point with coordinates 0 comma 0.

 

Question 314 314 of 368 selected Probability And Conditional Probability E

For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?

  1. 1 2,900

  2. 1 29

  3. 29 100

  4. 29 10

Show Answer Correct Answer: C

Choice C is correct. It’s given that 29 out of every 100 beads that the machine produces have a defect. It follows that if the machine produces k beads, then the number of beads that have a defect is 29100k, for some constant k . If a bead produced by the machine will be selected at random, the probability of selecting a bead that has a defect is given by the number of beads with a defect, 29100k, divided by the number of beads produced by the machine, k . Therefore, the probability of selecting a bead that has a defect is 29100kk, or 29100.

Choice A is incorrect and may result from conceptual or computational errors.

Choice B is incorrect and may result from conceptual or computational errors.

Choice D is incorrect and may result from conceptual or computational errors.

Question 315 315 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

The area of a rectangular region is increasing at a rate of 250 square feet per hour. Which of the following is closest to this rate in square meters per minute? (Use 1 meter=3.28 feet.)

  1. 0.39

  2. 1.27

  3. 13.67

  4. 23.24

Show Answer Correct Answer: A

Choice A is correct. It’s given that 1 meter=3.28 feet. It follows that 12 square meter=3.282 square feet, or 1 square meter=10.7584 square feet. Since 1 hour=60 minutes, it follows that 250 square feet per hour is equivalent to (250 square feet1 hour)(1 square meter10.7584 square feet)(1 hour60 minutes), or 250 square meters645.504 minutes, which is approximately 0.3873 square meters per minute. Of the given choices, 0.39 is closest to 0.3873 .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 316 316 of 368 selected Probability And Conditional Probability E

A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If the probability that a blue marble will be chosen is 0.35, how many marbles in the bag are blue?

  1. 21

  2. 25

  3. 35

  4. 39

Show Answer Correct Answer: A

Choice A is correct. Multiplying the number of marbles in the bag by the probability of selecting a blue marble gives the number of blue marbles in the bag. Since the bag contains a total of 60 marbles and the probability that a blue marble will be selected from the bag is 0.35, there are a total of 0 point 3 5 times 60, equals 21 blue marbles in the bag.

Choice B is incorrect and may result from subtracting 35 from 60. Choice C is incorrect. This would be the number of blue marbles in the bag if there were a total of 100 marbles, not 60 marbles. Choice D is incorrect. This is the number of marbles in the bag that aren’t blue.

Question 317 317 of 368 selected Two-Variable Data: Models And Scatterplots M

The scatterplot shows the relationship between two variables, x and y . A line of best fit for the data is also shown.

  • The scatterplot has 11 data points.
  • The data points are in a linear pattern trending down from left to right.
  • A line of best fit is shown:
    • The line of best fit slants down from left to right.
    • 6 points are above the line of best fit.
    • 5 points are below the line of best fit.
    • The line of best fit goes through the following approximate coordinates:
      • (28 comma 6)
      • (33 comma 1.5)

At x = 32 , which of the following is closest to the y-value predicted by the line of best fit?

  1. 0.4

  2. 1.5

  3. 2.4

  4. 3.3

Show Answer Correct Answer: C

Choice C is correct. At x=32, the line of best fit has a y-value between 2 and 3 . The only choice with a value between 2 and 3 is choice C.

Choice A is incorrect. This is the difference between the y-value predicted by the line of best fit and the actual y-value at x=32 rather than the y-value predicted by the line of best fit at x=32.

Choice B is incorrect. This is the y-value predicted by the line of best fit at x=31 rather than at x=32.

Choice D is incorrect. This is the y-value predicted by the line of best fit at x=33 rather than at x=32.

Question 318 318 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

An insect moves at a speed of 320 feet per second. What is this speed, in yards per second? (3 feet=1 yard)

  1. 1 20

  2. 9 20

  3. 6

  4. 20

Show Answer Correct Answer: A

Choice A is correct. It’s given that 3 feet=1 yard. It follows that a speed of 3 20 feet per second is equivalent to (320 feet1 second)(1 yard3 feet), which is equivalent to (320)(13), or 1 20 , yards per second.

Choice B is incorrect. This is the speed, in feet per second, that's equivalent to 3 20 yards per second.

Choice C is incorrect. This is the speed, in yards per second, that's equivalent to 18 , not 3 20 , feet per second.

Choice D is incorrect. This is the speed, in yards per second, that's equivalent to 60 , not 3 20 , feet per second.

Question 319 319 of 368 selected Percentages H

A scientist studying the life cycle of dragonflies counted the number of dragonflies in a certain habitat each day for 46 days. On February 15, there were 99 dragonflies in the habitat. The percent increase in the number of dragonflies in the habitat from January 1 to February 15 was 12.50%. How many dragonflies were in the habitat on January 1?

  1. 88

  2. 87

  3. 12

  4. 8

Show Answer Correct Answer: A

Choice A is correct. It’s given that a scientist studying the life cycle of dragonflies counted the number of dragonflies in a certain habitat each day for 46 days. It’s also given that on February 15 , there were 99 dragonflies in the habitat and that the percent increase in the number of dragonflies in the habitat from January 1 to February 15 was 12.50%. This can be represented by the equation
99=(1+12.50100)x, where x represents the number of dragonflies in the habitat on January 1 . This equation can be rewritten as 99=1.125x. Dividing both sides of this equation by 1.125 yields 88 = x . Therefore, there were 88 dragonflies in the habitat on January 1 .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 320 320 of 368 selected Probability And Conditional Probability E

On a street with 7 houses, 2 houses are blue. If a house from this street is selected at random, what is the probability of selecting a house that is blue?

  1. 17

  2. 27

  3. 57

  4. 77

Show Answer Correct Answer: B

Choice B is correct. If a house from the street is selected at random, the probability of selecting a house that is blue is equal to the number of houses on the street that are blue divided by the total number of houses on the street. Since there are 2 blue houses on a street with 7 total houses, the probability of selecting a house that is blue from this street is 2 7 .

Choice A is incorrect. This is the probability of selecting a house that is blue from a street on which 1 of the 7 houses is blue.

Choice C is incorrect. This is the probability of selecting a house that is not blue from this street.

Choice D is incorrect. This is the probability of selecting a house that is blue from a street on which all the houses are blue.

Question 321 321 of 368 selected Inference From Sample Statistics And Margin Of Error M

To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is 0.49 , with an associated margin of error of 0.04 . Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?

  1. It is plausible that the proportion is between 0.45 and 0.53 .

  2. It is plausible that the proportion is less than 0.45 .

  3. The proportion is exactly 0.49 .

  4. It is plausible that the proportion is greater than 0.53 .

Show Answer Correct Answer: A

Choice A is correct. It’s given that the estimate for the proportion of the population that has the characteristic is 0.49 with an associated margin of error of 0.04 . Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true proportion of the population that has the characteristic. Therefore, it’s plausible that the proportion of the population that has this characteristic is between 0.45 and 0.53 .

Choice B is incorrect. A value less than 0.45 is outside the interval of plausible values for the proportion of the population that has the characteristic.

Choice C is incorrect. The value 0.49 is an estimate for the proportion based on this sample. However, since the margin of error for this estimate is known, the most appropriate conclusion is not that the proportion is exactly one value but instead lies in an interval of plausible values.

Choice D is incorrect. A value greater than 0.53 is outside the interval of plausible values for the proportion of the population that has the characteristic.

Question 322 322 of 368 selected Inference From Sample Statistics And Margin Of Error M

A store manager reviewed the receipts from 80 customers who were selected at random from all the customers who made purchases last Thursday. Of those selected, 20 receipts showed that the customer had purchased fruit. If 1,500 customers made purchases last Thursday, which of the following is the most appropriate conclusion?

  1. Exactly 75 customers must have purchased fruit last Thursday.

  2. Exactly 375 customers must have purchased fruit last Thursday.

  3. The best estimate for the number of customers who purchased fruit last Thursday is 75.

  4. The best estimate for the number of customers who purchased fruit last Thursday is 375.

Show Answer Correct Answer: D

Choice D is correct. It’s given that the manager took a random selection of the receipts of 80 customers from a total of 1,500. It’s also given that of those 80 receipts, 20 showed that the customer had purchased fruit. This means that an appropriate estimate of the fraction of customers who purchased fruit is the fraction 20 over 80, or one fourth . Multiplying this fraction by the total number of customers yields one fourth times 1,500, equals 375. Therefore, the best estimate for the number of customers who purchased fruit is 375.

Choices A and B are incorrect because an exact number of customers can’t be known from taking a random selection. Additionally, choice A may also be the result of a calculation error. Choice C is incorrect and may result from a calculation error. 

 

Question 323 323 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H
 Masses (kilograms)
Andrew2.42.53.63.12.52.7
Mariax3.12.72.93.32.8
 

Andrew and Maria each collected six rocks, and the masses of the rocks are shown in the table above. The mean of the masses of the rocks Maria collected is 0.1 kilogram greater than the mean of the masses of the rocks Andrew collected. What is the value of x ?

Show Answer

The correct answer is 2.6. Since the mean of a set of numbers can be found by adding the numbers together and dividing by how many numbers there are in the set, the mean mass, in kilograms, of the rocks Andrew collected is the fraction with numerator 2 point 4, plus 2 point 5, plus 3 point 6, plus 3 point 1, plus 2 point 5, plus 2 point 7, and denominator 6, equals 16 point 8 over 6., or 2.8. Since the mean mass of the rocks Maria collected is 0.1 kilogram greater than the mean mass of rocks Andrew collected, the mean mass of the rocks Maria collected is 2 point 8, plus 0 point 1, equals 2 point 9 kilograms. The value of x can be found by writing an equation for finding the mean: the fraction with numerator x plus 3 point 1, plus 2 point 7, plus 2 point 9, plus 3 point 3, plus 2 point 8, and denominator 6, equals 2 point 9. Solving this equation gives x equals 2 point 6. Note that 2.6 and 13/5 are examples of ways to enter a correct answer.

 

 

Question 324 324 of 368 selected Inference From Sample Statistics And Margin Of Error E

In a study, the data from a random sample of a population had a mean of 37, with an associated margin of error of 3. Which of the following is the most appropriate conclusion that can be made about the population mean?

  1. It is less than 37.

  2. It is greater than 37.

  3. It is between 34 and 40.

  4. It is less than 34 or greater than 40.

Show Answer Correct Answer: C

Choice C is correct. It’s given that the mean of the data from a random sample of a population is 37, with an associated margin of error of 3. The most appropriate conclusion that can be made is that the mean of the entire population will fall between 37, plus or minus 3. Therefore, the population mean is between 37 minus 3, which equals 34 and 37 plus 3, which equals 40.

Choice A is incorrect. While it’s an appropriate conclusion that the population mean is as low as 37 minus 3, or 34, it isn’t appropriate to conclude that the population mean is less than 34. Choice B is incorrect. While it’s an appropriate conclusion that the population mean is as high as 37 plus 3, or 40, it isn’t appropriate to conclude that the population mean is greater than 40. Choice D is incorrect. It isn’t an appropriate conclusion that the population mean is less than 34 or greater than 40.

Question 325 325 of 368 selected Percentages E

What is 10% of 370 ?

  1. 27

  2. 37

  3. 333

  4. 360

Show Answer Correct Answer: B

Choice B is correct. 10% of a quantity means 10100 times the quantity. Therefore, 10% of 370 can be represented as 10100(370), which is equivalent to 0.10(370), or 37 . Therefore, 10% of 370 is 37 .

Choice A is incorrect. This is 10% of 270 , not 10% of 370 .

Choice C is incorrect. This is 90% of 370 , not 10% of 370 .

Choice D is incorrect. This is 370-10, not 10% of 370 .

Question 326 326 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E

The high temperature, in degrees Fahrenheit (°F), in a certain city was recorded for each of 5 days. The data are shown below.

Day 1 2 3 4 5
High temperature (°F) 81 80 81 81 82

Over this 5-day period, which of the following is NOT equal to 81°F?

  1. Median of the high temperatures

  2. Mean of the high temperatures

  3. Mode of the high temperatures

  4. Range of the high temperatures

Show Answer Correct Answer: D

Choice D is correct. The range of a data set is the difference between the maximum and the minimum values in the set. The maximum value among the high temperatures in the table is 82°F and the minimum value is 80°F. Therefore, the range is 82°F – 80°F = 2°F.

Choice A is incorrect. The median of a data set is the middle value when the values in the set are ordered from least to greatest. Ordering the high temperatures this way gives the list 80, 81, 81, 81, 82. Therefore, the median high temperature is 81°F. Choice B is incorrect. The mean high temperature is the fraction with numerator 81, plus 80, plus 81, plus 81, plus 82, and denominator 5, equals, the fraction 405 over 5, which equals 81. Choice C is incorrect. The mode is the value that occurs the greatest number of times. For the set of high temperatures shown, 81 is the value that occurs 3 times, and therefore, 81°F is the mode of the high temperatures.

Question 327 327 of 368 selected Inference From Sample Statistics And Margin Of Error H

Poll Results

Angel Cruz 483
Terry Smith 320

The table shows the results of a poll. A total of 803 voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if 6,424 people vote in the election, by how many votes would Angel Cruz be expected to win?

  1. 163

  2. 1,304

  3. 3,864

  4. 5,621

Show Answer Correct Answer: B

Choice B is correct. It's given that 483 out of 803 voters responded that they would vote for Angel Cruz. Therefore, the proportion of voters from the poll who responded they would vote for Angel Cruz is 483803. It’s also given that there are a total of 6,424 voters in the election. Therefore, the total number of people who would be expected to vote for Angel Cruz is 6,424(483803), or 3,864 . Since 3,864 of the 6,424 total voters would be expected to vote for Angel Cruz, it follows that 6,424-3,864, or 2,560 voters would be expected not to vote for Angel Cruz. The difference in the number of votes for and against Angel Cruz is 3,864-2,560, or 1,304 votes. Therefore, if 6,424 people vote in the election, Angel Cruz would be expected to win by 1,304 votes.

Choice A is incorrect. This is the difference in the number of voters from the poll who responded that they would vote for and against Angel Cruz.

Choice C is incorrect. This is the total number of people who would be expected to vote for Angel Cruz.

Choice D is incorrect. This is the difference between the total number of people who vote in the election and the number of voters from the poll.

Question 328 328 of 368 selected Inference From Sample Statistics And Margin Of Error E

An analyst collected data on the price of a carton of grape tomatoes at 30 locations selected at random in Utah. The mean price of a carton of grape tomatoes in Utah was estimated to be $4.23, with an associated margin of error of $0.08. Which of the following is a plausible statement about the mean price of a carton of grape tomatoes for all locations that sell this product in Utah?

  1. It is between $4.15 and $4.31.

  2. It is either less than $4.15 or greater than $4.31.

  3. It is less than $4.15.

  4. It is greater than $4.31.

Show Answer Correct Answer: A

Choice A is correct. It's given that the mean price of a carton of grape tomatoes in Utah was estimated to be $4.23, with an associated margin of error of $0.08. It follows that plausible values for this mean price are between $4.23-$0.08 and $4.23+$0.08. Therefore, it's plausible that the mean price of a carton of grape tomatoes for all locations that sell this product in Utah is between $4.15 and $4.31.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 329 329 of 368 selected Probability And Conditional Probability M

Penguin Exhibit

Type of penguin Male Female Total
     Chinstrap   41   59 100
     Emperor     8   27   35
     Gentoo   49   54 103
     Macaroni   42   40   82
     Total 140 180 320

The number of penguins in a zoo exhibit, sorted by gender and type of penguin, is shown in the table above. Which type of penguin has a female population that is the closest to being one-third of the total female penguin population in the exhibit?

  1. Chinstrap

  2. Emperor

  3. Gentoo

  4. Macaroni

Show Answer Correct Answer: A

Choice A is correct. It is given that there are 180 female penguins in the exhibit. Therefore, one third  of the female penguins is one third times 180, equals 60 penguins. According to the table, there are 59 female chinstrap penguins, 27 female emperor penguins, 54 female gentoo penguins, and 40 female macaroni penguins. So the female chinstrap penguin population is the closest to 60, or one third of the total female population in the exhibit.

Choices B, C, and D are incorrect and may result from reading data from the table incorrectly. Since the total female penguin population is 180, one third of the total female penguin population is 60. The numbers of female emperor (27), female gentoo (54), and female macaroni (40) penguins are not as close to 60 as the number of female chinstrap penguins (59).

Question 330 330 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread E
Number of High School Students Who
Completed Summer Internships
High schoolYear
20082009201020112012
Foothill8780757670
Valley4454657682
Total131134140152152

The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Which of the following statements are true about the number of students who completed summer internships for the 5 years shown?

  1. The mean number from Foothill High School is greater than the mean number from Valley High School.
  2. The median number from Foothill High School is greater than the median number from Valley High School.

  1. I only

  2. II only

  3. I and II

  4. Neither I nor II

Show Answer Correct Answer: C

Choice C is correct. The mean of a data set is found by dividing the sum of the values by the number of values. Therefore, the mean number of students who completed summer internships from Foothill High School is the fraction with numerator 87 plus 80, plus 75, plus 76, plus 70, and denominator 5, equals, the fraction 388 over 5, or 77.6. Similarly, the mean number from Valley High School is the fraction with numerator 44 plus 54, plus 65, plus 76, plus 82, and denominator 5, equals, the fraction 321 over 5, or 64.2. Thus, the mean number from Foothill High School is greater than the mean number from Valley High School. When a data set has an odd number of elements, the median can be found by ordering the values from least to greatest and determining the value in the middle. Since there are five values in each data set, the third value in each ordered list is the median. Therefore, the median number from Foothill High School is 76 and the median number from Valley High School is 65. Thus, the median number from Foothill High School is greater than the median number from Valley High School.

Choices A, B, and D are incorrect and may result from various misconceptions or miscalculations.

Question 331 331 of 368 selected Probability And Conditional Probability E

-13 , 4 , 23

A data set of three numbers is shown. If a number from this data set is selected at random, what is the probability of selecting a negative number?

  1. 0

  2. 1 3

  3. 2 3

  4. 1

Show Answer Correct Answer: B

Choice B is correct. If a number from the data set is selected at random, the probability of selecting a negative number is the count of negative numbers in the data set divided by the total count of numbers in the data set. It's given that a data set of three numbers is shown. It follows that the total count of numbers in the data set is 3 . In the data set shown, - 13 is the only negative number. It follows that the count of negative numbers in the data set is 1 . Therefore, if a number from the data set is selected at random, the probability of selecting a negative number is 13.

Choice A is incorrect. This is the probability of selecting a negative number from a data set that doesn’t contain any negative numbers.

Choice C is incorrect. This is the probability of selecting a positive number, not a negative number, from the data set.

Choice D is incorrect. This is the probability of selecting a negative number from a data set that contains only negative numbers.

Question 332 332 of 368 selected Two-Variable Data: Models And Scatterplots H

For x>0, the function f is defined as follows:

f(x) equals 201% of x

Which of the following could describe this function?

  1. Decreasing exponential

  2. Decreasing linear

  3. Increasing exponential

  4. Increasing linear

Show Answer Correct Answer: D

Choice D is correct. It's given that for x>0, f(x) is equal to 201% of x . This is equivalent to f(x)=201100x, or f(x)=2.01x, for x>0. This function indicates that as x increases, f(x) also increases, which means f is an increasing function. Furthermore,  f(x) increases at a constant rate of 2.01 for each increase of x by 1 . A function with a constant rate of change is linear. Thus, the function f can be described as an increasing linear function.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect. This could describe the function f(x)=(2.01)x, where f(x) is equal to 201% of f(x-1), not x , for x>0.

Question 333 333 of 368 selected Probability And Conditional Probability E

There are 20 buttons in a bag: 8 white buttons, 2 orange buttons, and 10 brown buttons. If one of these buttons is selected at random, what is the probability of selecting a white button?

  1. 220

  2. 820

  3. 1020

  4. 1220

Show Answer Correct Answer: B

Choice B is correct. It’s given that there are 20 buttons in a bag and 8 of the buttons are white. If one button from the bag is selected at random, the probability of selecting a white button is the number of white buttons in the bag divided by the total number of buttons in the bag. Therefore, if one button from the bag is selected at random, the probability of selecting a white button is 820.

Choice A is incorrect. This is the probability of selecting an orange button from the bag.

Choice C is incorrect. This is the probability of selecting a brown button from the bag.

Choice D is incorrect. This is the probability of selecting a button that isn't white from the bag.

Question 334 334 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

If t equals 4 u , which of the following is equivalent to 2 t ?

  1. 8 u

  2. 2 u

  3. u

  4. one-half u

Show Answer Correct Answer: A

Choice A is correct. It’s given that t equals 4 u. Multiplying both sides of this equation by 2 yields 2 t equals, 2 times, 4 u, or 2 t equals 8 u.

Choice B is incorrect and may result from dividing, instead of multiplying, the right-hand side of the equation by 2. Choices C and D are incorrect and may result from calculation errors.

 

Question 335 335 of 368 selected Two-Variable Data: Models And Scatterplots H
Amount invested Balance increase
Account A    $500 6% annual interest
Account B $1,000 $25 per year

Two investments were made as shown in the table above. The interest in Account A is compounded once per year. Which of the following is true about the investments?

  1. Account A always earns more money per year than Account B.

  2. Account A always earns less money per year than Account B.

  3. Account A earns more money per year than Account B at first but eventually earns less money per year.

  4. Account A earns less money per year than Account B at first but eventually earns more money per year.

Show Answer Correct Answer: A

Choice A is correct. Account A starts with $500 and earns interest at 6% per year, so in the first year Account A earns (500)(0.06) = $30, which is greater than the $25 that Account B earns that year. Compounding interest can be modeled by an increasing exponential function, so each year Account A will earn more money than it did the previous year. Therefore, each year Account A earns at least $30 in interest. Since Account B always earns $25 each year, Account A always earns more money per year than Account B.

Choices B and D are incorrect. Account A earns $30 in the first year, which is greater than the $25 Account B earns in the first year. Therefore, neither the statement that Account A always earns less money per year than Account B nor the statement that Account A earns less money than Account B at first can be true. Choice C is incorrect. Since compounding interest can be modeled by an increasing exponential function, each year Account A will earn more money than it did the previous year. Therefore, Account A always earns at least $30 per year, which is more than the $25 per year that Account B earns.

Question 336 336 of 368 selected Percentages M

Thomas installed a new stove in his restaurant. At the time of installation, the stove had a value of $800. Thomas estimates that each year the value of the stove will depreciate by 20% of the previous year’s estimated value. What is the estimated value of the stove exactly 2 years after Thomas installed it?

  1. $480

  2. $512

  3. $556

  4. $640

Show Answer Correct Answer: B

Choice B is correct. If the stove’s value depreciates by 20% of the previous year’s estimated value, then each year it retains 100% – 20% = 80%, or 0.80, of the previous year’s estimated value. Since the stove’s value was $800 when Thomas installed it, the estimated value after two years would be (0.80)(0.80)($800) = $512.

Choice A is incorrect. This is the value of the stove if each year it had depreciated by 20% of the original value rather than by 20% of the previous year’s estimated value. Choice C is incorrect and may be the result of a computational error. Choice D is incorrect. This is the estimated value of the stove 1 year after Thomas installed it, not 2 years.

 

Question 337 337 of 368 selected Percentages E

Rita’s total bill at a restaurant was $25.00, including tax. If she left a tip of 20% of the total bill, what was the amount of the tip?

  1. $3.50

  2. $4.00

  3. $4.50

  4. $5.00

Show Answer Correct Answer: D

Choice D is correct. The total bill was $25.00. The percentage 20% is equivalent to the decimal 0.2. The tip is the product of the percentage and the total bill; therefore, 0 point 2 times 25, equals 5, so the tip was $5.00.

Choices A, B, and C are incorrect and may be the result of incorrectly converting the given percentage or a calculation error.

Question 338 338 of 368 selected Percentages M

The number of coins in a collection increased from 9 to 90 . What was the percent increase in the number of coins in this collection?

  1. 10%

  2. 81%

  3. 90%

  4. 900%

Show Answer Correct Answer: D

Choice D is correct. It's given that the number of coins in the collection increased from 9 to 90 . It follows that the number of coins in the collection increased by 90-9, or 81 . Let x% represent the percentage that 81 is of 9 . The value of x can be found using the proportion 819=x100, or 9=x100. Multiplying both sides of this equation by 100 yields 900=x. Thus, when the number of coins in the collection increased from 9 to 90 , the percent increase was 900%.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 339 339 of 368 selected Percentages H

The regular price of a shirt at a store is $11.70 . The sale price of the shirt is 80 % less than the regular price, and the sale price is 30 % greater than the store's cost for the shirt. What was the store’s cost, in dollars, for the shirt? (Disregard the $ sign when entering your answer. For example, if your answer is $4.97 , enter 4.97 )

Show Answer Correct Answer: 1.8, 9/5

The correct answer is 1.8 . It’s given that the regular price of a shirt at a store is $11.70, and the sale price of the shirt is 80% less than the regular price. It follows that the sale price of the shirt is $11.70(1-80100), or $11.70(1-0.8), which is equivalent to $2.34. It’s also given that the sale price of the shirt is 30% greater than the store’s cost for the shirt. Let x represent the store’s cost for the shirt. It follows that 2.34=(1+30100)x, or 2.34=1.3x. Dividing both sides of this equation by 1.3 yields x=1.80. Therefore, the store’s cost, in dollars, for the shirt is 1.80. Note that 1.8 and 9/5 are examples of ways to enter a correct answer.

Question 340 340 of 368 selected Inference From Sample Statistics And Margin Of Error M

A random sample of 400 town voters were asked if they plan to vote for Candidate A or Candidate B for mayor. The results were sorted by gender and are shown in the table below.

 Plan to vote for Candidate APlan to vote for Candidate B
Female20220
Male34144

The town has a total of 6,000 voters. Based on the table, what is the best estimate of the number of voters who plan to vote for Candidate A?

 

Show Answer

The correct answer is 3,540. According to the table, of 400 voters randomly sampled, the total number of men and women who plan to vote for Candidate A is 202 plus 34 equals 236. The best estimate of the total number of voters in the town who plan to vote for Candidate A is the fraction of voters in the sample who plan to vote for Candidate A, the fraction 236 over 400, multiplied by the total voter population of 6000. Therefore, the answer is open parenthesis, the fraction 236 over 400, close parenthesis, times, 6000, equals 3540.

Question 341 341 of 368 selected Percentages E

What number is 20% greater than 60 ?

  1. 50

  2. 72

  3. 75

  4. 132

Show Answer Correct Answer: B

Choice B is correct. The decimal equivalent of 20% is 0.2. The number that is 20% greater than 60 is also 120% of 60. The decimal equivalent of 120% is 1.2, and 1 point 2 times 60, equals 72.

Alternate approach: 10% of 60 is 6, and 20% of 60 is double that amount, or 12. It follows that the number that is 20% greater than 60 is 12 more than 60, or 60 plus 12, equals 72.

Choice A is incorrect and may result from dividing, instead of multiplying, 60 by 1.2. Choice C is incorrect because it’s 25% greater than 60, rather than 20% greater than 60. Choice D is incorrect and may result from multiplying 60 by 2.2 instead of 1.2.

 

Question 342 342 of 368 selected Percentages E

Out of 300 seeds that were planted, 80% sprouted. How many of these seeds sprouted?

Show Answer Correct Answer: 240

The correct answer is 240 . It’s given that 80% of the 300 seeds sprouted. Therefore, the number of seeds that sprouted can be calculated by multiplying the number of seeds that were planted by 80100, which gives 300(80100), or 240 .

Question 343 343 of 368 selected Probability And Conditional Probability M

A box contains 13 red pens and 37 blue pens. If one of these pens is selected at random, what is the probability of selecting a red pen? (Express your answer as a decimal or fraction, not as a percent.)

Show Answer Correct Answer: .26, 13/50

The correct answer is 1350. It's given that a box contains 13 red pens and 37 blue pens. If one of these pens is selected at random, the probability of selecting a red pen is the number of red pens in the box divided by the number of red and blue pens in the box. The number of red and blue pens in the box is 13+37, or 50 . Since there are 13 red pens in the box, it follows that the probability of selecting a red pen is 13 50 . Note that 13/50 and .26 are examples of ways to enter a correct answer.

Question 344 344 of 368 selected Percentages H

According to a set of standards, a certain type of substance can contain a maximum of 0.001% phosphorus by mass. If a sample of this substance has a mass of 140 grams, what is the maximum mass, in grams, of phosphorus the sample can contain to meet these standards?

Show Answer Correct Answer: .0014

The correct answer is .0014. It's given that a certain type of substance can contain a maximum of 0.001% phosphorus by mass to meet a set of standards. If a sample of the substance has a mass of 140 grams, it follows that the maximum mass, in grams, of phosphorus the sample can contain to meet the standards is 0.001% of 140 , or 0.001100(140), which is equivalent to (0.00001)(140), or 0.0014 . Note that .0014 and 0.001 are examples of ways to enter a correct answer.

Question 345 345 of 368 selected Probability And Conditional Probability M
Human Resources Accounting
Bachelor’s degree 4 3
Master’s degree 2 6

The table above shows the number of people who work in the Human Resources and Accounting departments of a company and the highest level of education they have completed. A person from one of these departments is to be chosen at random. If the person chosen works in the Human Resources department, what is the probability that the highest level of education the person completed is a master’s degree?

  1. the fraction 2 over 15
  2. one-third
  3. one-fourth
  4. the fraction 8 over 15
Show Answer Correct Answer: B

Choice B is correct. In total, there are 6 people in the Human Resources department. Of those 6, 2 have a master’s degree as their highest level of education. Therefore, the probability of an employee selected at random from the Human Resources department having a master’s degree is  two sixths, which simplifies to one third.

Choice A is incorrect; it is the probability that an employee selected at random from either department will be in the Human Resources department and have a master’s degree. Choice C is incorrect; it is the probability that an employee with a master’s degree selected at random will be in the Human Resources department. Choice D is incorrect; it is the probability that an employee selected at random from either department will have a master’s degree.

Question 346 346 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the temperature, in degrees Fahrenheit (°F), and the distance above sea level, in feet, measured at 6 locations on Mount Jefferson. A line of best fit is also shown.

2,0004,0006,0008,000x1020304050607080yODistance above sea level (feet)Temperature (°F)
  • The scatterplot has 6 data points.
  • The data points are in a linear pattern trending down from left to right.
  • A line of best fit is shown:
    • The line of best fit slants down from left to right.
    • The line of best fit passes through the following coordinates:
      • (0 comma 47)
      • (4,000 comma 35)
      • (7,000 comma 26)

At a distance of 4,000 feet above sea level, what is the temperature, in °F, predicted by the line of best fit?

  1. 47

  2. 35

  3. 25

  4. 0

Show Answer Correct Answer: B

Choice B is correct. In the given scatterplot, the x-values represent the distance above sea level, in feet, and the y-values represent the temperature, in °F. The point on the line of best fit with an x-value of 4,000 has a corresponding y-value of 35 . Therefore, at a distance of 4,000 feet above sea level, the temperature predicted by the line of best fit is 35°F.

Choice A is incorrect. This is the temperature, in °F, predicted by the line of best fit at a distance of 0 feet above sea level.

Choice C is incorrect. This is the measured temperature, in °F, at a distance of 6,000 feet above sea level.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 347 347 of 368 selected Two-Variable Data: Models And Scatterplots M

The scatterplot shows the relationship between two variables, x and y .

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending down from left to right.
  • The data points have the following approximate coordinates:
    • (0 comma 10)
    • (1.2 comma 9)
    • (2.3 comma 8)
    • (3.1 comma 5)
    • (4.8 comma 5)
    • (5.2 comma 3)
    • (6.5 comma 3)
    • (7.2 comma 3)
    • (9.6 comma 2)
    • (8.8 comma 1)

Which of the following equations is the most appropriate linear model for the data shown?

  1. y=0.9+ 9.4 x

  2. y=0.9- 9.4 x

  3. y=9.4 +0.9x

  4. y=9.4 -0.9x

Show Answer Correct Answer: D

Choice D is correct. The data points suggest that as the variable x increases, the variable y decreases, which implies that an appropriate linear model for the data has a negative slope. The data points also show that when x is close to 0 , y is greater than 9 . Therefore, the y-intercept of the graph of an appropriate linear model has a y-coordinate greater than 9 . The graph of an equation of the form y=a+bx, where a and b are constants, has a y-intercept with a y-coordinate of a and has a slope of b . Of the given choices, only choice D represents a graph that has a negative slope, -0.9 , and a y-intercept with a y-coordinate greater than 9 , 9.4 .

Choice A is incorrect. The graph of this equation has a positive slope, not a negative slope, and a y-intercept with a y-coordinate less than 1 , not greater than 9 .

Choice B is incorrect. The graph of this equation has a y-intercept with a y-coordinate less than 1 , not greater than 9 .

Choice C is incorrect. The graph of this equation has a positive slope, not a negative slope.

Question 348 348 of 368 selected Percentages H

37 % of the items in a box are green. Of those, 37 % are also rectangular. Of the green rectangular items, 42 % are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?

  1. 1.16 %

  2. 57.50 %

  3. 94.25 %

  4. 98.84 %

Show Answer Correct Answer: C

Choice C is correct. It's given that 37% of the items in a box are green. Let x represent the total number of items in the box. It follows that 37100x, or 0.37x, items in the box are green. It's also given that of those, 37% are also rectangular. Therefore, 37100(0.37x), or 0.1369x, items in the box are green rectangular items. It's also given that of the green rectangular items, 42% are also metal. Therefore, 42100(0.1369x), or 0.057498x, items in the box are rectangular green metal items. The number of the items in the box that are not rectangular green metal items is the total number of items in the box minus the number of rectangular green metal items in the box. Therefore, the number of items in the box that are not rectangular green metal items is x-0.057498x, or 0.942502x. The percentage of items in the box that are not rectangular green metal items is the percentage that 0.942502x is of x . If p% represents this percentage, the value of p is 100(0.942502xx), or 94.2502. Of the given choices, 94.25% is closest to the percentage of items in the box that are not rectangular green metal items.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 349 349 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use?

  1. Exactly 5 ounces

  2. 3 ounces more than the amount of yellow paint used in the first batch

  3. 1.5 times the amount of yellow paint used in the first batch

  4. 1.5 times the amount of blue paint used in the second batch

Show Answer Correct Answer: D

Choice D is correct. It’s given that Anita used a ratio of 2 ounces of blue paint to 3 ounces of yellow paint for the first batch. For any batch of paint that uses the same ratio, the amount of yellow paint used will be three halves, or 1.5, times the amount of blue paint used in the batch. Therefore, the amount of yellow paint Anita will use in the second batch will be 1.5 times the amount of blue paint used in the second batch.

Alternate approach: It’s given that Anita used a ratio of 2 ounces of blue paint to 3 ounces of yellow paint for the first batch and that she will use 5 ounces of blue paint for the second batch. A proportion can be set up to solve for x, the amount of yellow paint she will use for the second batch: 2 over 3, equals, 5 over x. Multiplying both sides of this equation by 3 yields 2 equals, 15 over x, and multiplying both sides of this equation by x yields 2 x equals 15. Dividing both sides of this equation by 2 yields x equals 7 point 5. Since Anita will use 7.5 ounces of yellow paint for the second batch, this is 7 point 5 over 5 equals 1 point 5 times the amount of blue paint (5 ounces) used in the second batch.

Choices A, B, and C are incorrect and may result from incorrectly interpreting the ratio of blue paint to yellow paint used.

 

Question 350 350 of 368 selected One-Variable Data: Distributions And Measures Of Center And Spread H

For a certain computer game, individuals receive an integer score that ranges from 2 through 10. The table below shows the frequency distribution of the scores of the 9 players in group A and the 11 players in group B.

ScoreScore Frequencies
Group AGroup B
210
310
420
514
632
700
802
911
1002
Total911

 

 

The median of the scores for group B is how much greater than the median of the scores for group A?

Show Answer

The correct answer is 1. When there are an odd number of values in a data set, the median of the data set is the middle number when the data values are ordered from least to greatest. The scores for group A, ordered from least to greatest, are 2, 3, 4, 4, 5, 6, 6, 6, and 9. The median of the scores for group A is therefore 5. The scores for group B, ordered from least to greatest, are 5, 5, 5, 5, 6, 6, 8, 8, 9, 10, and 10. The median of the scores for group B is therefore 6. The median score for group B is 6 minus 5, equals 1 more than the median score for group A.

Question 351 351 of 368 selected Two-Variable Data: Models And Scatterplots M

The scatterplot shows the relationship between two variables, x and y . A line of best fit is also shown.

  • The scatterplot has 5 data points.
  • The data points are in a linear pattern trending down from left to right.
  • A line of best fit is shown:
    • The line of best fit slants down from left to right.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 14.1)
      • (12.7 comma 0)

Which of the following is closest to the slope of this line of best fit?

  1. -3.3

  2. -1.1

  3. 1.1

  4. 3.3

Show Answer Correct Answer: B

Choice B is correct. A line in the xy-plane that passes through points (x1,y1) and (x2,y2) has a slope of y2-y1x2-x1. The line of best fit shown passes approximately through the points (0,14) and (13,0). It follows that the slope of this line of best fit is approximately 0-1413-0, or -1413. Of the given choices, - 1.1 is closest to -1413.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 352 352 of 368 selected Two-Variable Data: Models And Scatterplots H
The figure presents a scatterplot titled “Total Protein and Total Fat for Eight Sandwiches.” The horizontal axis is labeled “Total protein,” in grams, and the numbers zero through 50, in increments of 10, are indicated. The vertical axis is labeled “Total fat,” in grams, and the numbers zero through 80, in increments of 10, are indicated. Eight data points and the line of best fit are shown. The line of best fit touches all 8 data points and extends upward and to the right through the following coordinates. All data are approximate. 

Protein, 9 grams; Fat, 17 grams.
Protein, 20 grams; Fat, 33 grams.
Protein, 30 grams; Fat, 48 grams.
Protein, 40 grams; Fat, 63 grams.
Protein, 48 grams; Fat, 75 grams.

The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?

  1. 2.5

  2. 2.0

  3. 1.5

  4. 1.0

Show Answer Correct Answer: C

Choice C is correct. The predicted increase in total fat, in grams, for every increase of 1 gram in total protein is represented by the slope of the line of best fit. Any two points on the line can be used to calculate the slope of the line as the change in total fat over the change in total protein. For instance, it can be estimated that the points with coordinates 20 comma 34 and with coordinates 30 comma 48 are on the line of best fit, and the slope of the line that passes through them is the fraction with numerator 48 minus 34, and denominator 30 minus 20, end fraction, equals 14 over 10, or 1.4. Of the choices given, 1.5 is the closest to the slope of the line of best fit.

Choices A, B, and D are incorrect and may be the result of incorrectly finding ordered pairs that lie on the line of best fit or of incorrectly calculating the slope.

 

Question 353 353 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the relationship between x and y . A line of best fit is also shown.

  • The scatterplot has 6 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • 1 point is touching the line of best fit.
    • 2 points are above the line of best fit.
    • 3 points are below the lines of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 0.2)
      • (4 comma 2)

Which of the following is closest to the slope of the line of best fit shown?

  1. -2.27

  2. -0.44

  3. 0.44

  4. 2.27

Show Answer Correct Answer: C

Choice C is correct. It's given that the scatterplot shows the relationship between two variables, x and y , and a line of best fit is shown. For the line of best fit shown, for each increase in the value of x by 1 , the corresponding value of y increases by a constant rate. It follows that the relationship between the variables x and y has a positive linear trend. A line in the xy-plane that passes through the points (a,b) and (c,d) has a slope of d-bc-a. The line of best fit shown passes approximately through the points (0,0.25) and (4,2). It follows that the slope of this line is approximately 2-0.254-0, which is equivalent to 0.4375 . Therefore, of the given choices, 0.44 is closest to the slope of the line of best fit shown.

Choice A is incorrect. This is the slope of a line of best fit for a relationship between x and y that has a negative, rather than a positive, linear trend.

Choice B is incorrect. This is the slope of a line of best fit for a relationship between x and y that has a negative, rather than a positive, linear trend.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 354 354 of 368 selected Two-Variable Data: Models And Scatterplots M

Each year, the value of an investment increases by 0.49 % of its value the previous year. Which of the following functions best models how the value of the investment changes over time?

  1. Decreasing exponential

  2. Decreasing linear

  3. Increasing exponential

  4. Increasing linear

Show Answer Correct Answer: C

Choice C is correct. Because the value of the investment increases each year, the function that best models how the value of the investment changes over time is an increasing function. It′s given that each year, the value of the investment increases by 0.49% of its value the previous year. Since the value of the investment changes by a fixed percentage each year, the function that best models how the value of the investment changes over time is an exponential function. Therefore, the function that best models how the value of the investment changes over time is an increasing exponential function.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.

Question 355 355 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

How many yards are equivalent to 1,116 inches? (1 yard=36 inches)

Show Answer Correct Answer: 31

The correct answer is 31 . It's given that 1 yard is equal to 36 inches. Therefore, 1,116 inches is equivalent to (1,116 inches)(1 yard36 inches), or 31 yards.

Question 356 356 of 368 selected Ratios, Rates, Proportional Relationships, And Units H

A certain park has an area of 11,863,808 square yards. What is the area, in square miles, of this park? (1 mile=1,760 yards)

  1. 1.96

  2. 3.83

  3. 3,444.39  

  4. 6,740.8

Show Answer Correct Answer: B

Choice B is correct. Since 1 mile is equal to 1,760 yards, 1 square mile is equal to 1,7602, or 3,097,600, square yards. It’s given that the park has an area of 11,863,808 square yards. Therefore, the park has an area of (11,863,808 square yards)(1 square mile3,097,600 square yards), or 11,863,8083,097,600 square miles. Thus, the area, in square miles, of the park is 3.83 .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the square root of the area of the park in square yards, not the area of the park in square miles.

Choice D is incorrect and may result from converting 11,863,808 yards to miles, rather than converting 11,863,808 square yards to square miles.

Question 357 357 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

How many teaspoons are equivalent to 44 tablespoons? (3 teaspoons=1 tablespoon)

  1. 47

  2. 88

  3. 132

  4. 176

Show Answer Correct Answer: C

Choice C is correct. It's given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 44 tablespoons is equivalent to (44 tablespoons)(3 teaspoons1 tablespoon), or 132 teaspoons.

Choice A is incorrect. This is equivalent to approximately 15.66 tablespoons, not 44 tablespoons.

Choice B is incorrect. This is equivalent to approximately 29.33 tablespoons, not 44 tablespoons.

Choice D is incorrect. This is equivalent to approximately 58.66 tablespoons, not 44 tablespoons.

Question 358 358 of 368 selected Ratios, Rates, Proportional Relationships, And Units M

For a certain rectangular region, the ratio of its length to its width is 35 to 10 . If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?

  1. It must decrease by 24.5 units.

  2. It must increase by 24.5 units.

  3. It must decrease by 7 units.

  4. It must increase by 7 units.

Show Answer Correct Answer: B

Choice B is correct. It’s given that the ratio of the rectangular region’s length to its width is 35 to 10 . This can be written as a proportion: lengthwidth=3510, or lw=3510. This proportion can be rewritten as 10l=35w, or l=3.5w. If the width of the rectangular region increases by 7 , then the length will increase by some number x in order to maintain this ratio. The value of x can be found by replacing l with l+x and w with w + 7 in the equation, which gives l+x=3.5(w+7). This equation can be rewritten using the distributive property as l+x=3.5w+24.5. Since l=3.5w, the right-hand side of this equation can be rewritten by substituting l for 3.5 w , which gives l+x=l+24.5, or x = 24.5 . Therefore, if the width of the rectangular region increases by 7 units, the length must increase by 24.5 units in order to maintain the given ratio.

Choice A is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease.

Choice C is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease.

Choice D is incorrect. Since the ratio of the length to the width of the rectangular region is 35 to 10 , if the width of the rectangular region increases by 7 units, the length would have to increase by a proportional amount, which would have to be greater than 7 units.

Question 359 359 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

The ratio x to y is equivalent to the ratio 12 to t . When x = 156 , what is the value of y in terms of t ?

  1. 13 t

  2. 12 t

  3. 144 t

  4. 168 t

Show Answer Correct Answer: A

Choice A is correct. It's given that the ratio x to y is equivalent to the ratio 12 to t . This can be represented by xy=12t. Substituting 156 for x in this equation yields 156y=12t. This can be rewritten as 12y=156t. Dividing both sides of this equation by 12 yields y = 13 t . Therefore, when x = 156 , the value of y in terms of t is 13 t .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 360 360 of 368 selected Percentages H

The number a is 60 % greater than the positive number b . The number c is 45 % less than a . The number c is how many times b ?

Show Answer Correct Answer: .88, 22/25

The correct answer is .88. It’s given that the number a is 60% greater than the positive number b . Therefore, a=(1+60100)b, which is equivalent to a=(1+0.60)b, or  a = 1.60 b . It’s also given that the number c is 45% less than a . Therefore, c=(1-45100)a, which is equivalent to c=(1-0.45)a, or c = 0.55 a . Since a = 1.60 b , substituting 1.60 b for a in the equation c = 0.55 a yields c=0.55(1.60b), or c = 0.88 b . Thus, the number c is 0.88 times the number b . Note that .88 and 22/25 are examples of ways to enter a correct answer. 

Question 361 361 of 368 selected Percentages H

The value of a collectible comic book increased by 167% from the end of 2011 to the end of 2012 and then decreased by 16% from the end of 2012 to the end of 2013. What was the net percentage increase in the value of the collectible comic book from the end of 2011 to the end of 2013?

  1. 124.28%

  2. 140.28%

  3. 151.00%

  4. 209.72%

Show Answer Correct Answer: A

Choice A is correct. It’s given that the value of the comic book increased by 167% from the end of 2011 to the end of 2012. Therefore, if the value of the comic book at the end of 2011 was x dollars, then the value, in dollars, of the comic book at the end of 2012 was x+(167100)x, which can be rewritten as 1x+1.67x, or 2.67 x . It’s also given that the value of the comic book decreased by 16% from the end of 2012 to the end of 2013. Therefore, the value, in dollars, of the comic book at the end of 2013 was 2.67x-2.67x(16100), which can be rewritten as 2.67x-(2.67x)(0.16), or 2.2428x. Thus, if the value of the comic book at the end of 2011 was x dollars, and the value of the comic book at the end of 2013 was 2.2428 x dollars, then from the end of 2011 to the end of 2013, the value of the comic book increased by 2.2428x-1x, or 1.2428 x , dollars. Therefore, the increase in the value of the comic book from the end of 2011 to the end of 2013 is equal to 1.2428 times the value of the comic book at the end of 2011. It follows that from the end of 2011 to the end of 2013, the net percentage increase in the value of the comic book was (1.2428)(100)%, or 124.28%.

Choice B is incorrect and may result from conceptual or calculation errors. 

Choice C is incorrect. This is the difference between the net percentage increase in the value of the comic book from the end of 2011 to the end of 2012 and the net percentage decrease in the value of the comic book from the end of 2012 to the end of 2013, not the net percentage increase in the value of the comic book from the end of 2011 to the end of 2013.

Choice D is incorrect. This is the net percentage increase in the value of the comic book from the end of 2011 to the end of 2013, if the value of the comic book increased by 167% from the end of 2011 to the end of 2012 and then increased, not decreased, by 16% from the end of 2012 to the end of 2013.

Question 362 362 of 368 selected Probability And Conditional Probability H

Employees working for a customer service line at an electric company recorded all the calls last Monday and noted whether the caller asked for repairs and whether the caller asked about a bill. The results are summarized in the table below.

Asked for
 repairs
Did not ask
 for repairs
Total
Asked
 about a bill
48 623 671
Did not ask
 about a bill
130 90 220
Total 178 713 891

If a caller last Monday who asked about his or her bill is selected at random, which of the following is closest to the probability that the customer also asked for repairs?

  1. 0.05

  2. 0.07

  3. 0.20

  4. 0.27

Show Answer Correct Answer: B

Choice B is correct. According to the table, a total of 671 customers asked about a bill. Of these, 48 also asked for repairs. Therefore, if a customer who asked about a bill is selected at random, the probability that the customer also asked for repairs is 48 over 671 is approximately equal to 0 point 0 7.

Choice A is incorrect. This is the probability that a customer selected at random from all customers who called on Monday both asked for repairs and asked about a bill. Choice C is incorrect. This is the probability that a customer selected at random from all customers who called on Monday asked for repairs, regardless of whether or not the customer asked about a bill. Choice D is incorrect. This is the probability that a customer selected at random from those who asked for repairs also asked about a bill.

Question 363 363 of 368 selected Two-Variable Data: Models And Scatterplots E

The scatterplot shows the relationship between the weight, in pounds, of each of 9 female gray wolves on April 30 and the number of offspring each gray wolf produced.

  • The scatterplot has 9 data points.
  • The data points are in a linear pattern trending up from left to right.
  • The data points have the following coordinates:
    • (40 comma 5)
    • (43 comma 5)
    • (47 comma 6)
    • (50 comma 6)
    • (53 comma 7)
    • (55 comma 6)
    • (60 comma 7)
    • (64 comma 7)
    • (66 comma 8)

How many offspring did the 50 -pound gray wolf produce?

  1. 8

  2. 7

  3. 6

  4. 5

Show Answer Correct Answer: C

Choice C is correct. For each point on the scatterplot shown, the x-value represents the weight, in pounds, of a female gray wolf and the y-value represents the number of offspring that wolf produced. The point on the graph with an x-value of 50 has a y-value of 6 . Therefore, the 50 -pound gray wolf produced 6 offspring.

Choice A is incorrect. One of the wolves produced 8 offspring, but its weight was greater than 50 pounds.

Choice B is incorrect. Three of the wolves produced 7 offspring each, but their weights were each greater than 50 pounds.

Choice D is incorrect. Two of the wolves produced 5 offspring each, but their weights were each less than 50 pounds.

Question 364 364 of 368 selected Percentages M

In March, the price of a collectible card was $15.50. In April, the price of the collectible card was $17.36. The price of the collectible card in April was p% of the price of the collectible card in March. What is the value of p ?

  1. 12

  2. 88

  3. 112

  4. 188

Show Answer Correct Answer: C

Choice C is correct. It's given that the price of the collectible card was $15.50 in March and $17.36 in April. It's also given that the price of the collectible card in April was p% of the price in March. It follows that $17.36 is p% of $15.50. Therefore, the value of p can be calculated by solving the equation 17.36=(p100)(15.50), or 17.36=15.50p100. Multiplying each side of this equation by 100 yields 1,736=15.50p. Dividing each side of this equation by 15.50 yields 112 = p . Therefore, the value of p is 112 .

Choice A is incorrect. 12% is the percent increase in the price of the collectible card from March to April.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 365 365 of 368 selected Two-Variable Data: Models And Scatterplots E

The figure presents a scatterplot titled “Distance and Density of Planetoids in the Inner Solar System.” The horizontal axis is labeled “Distance from the Sun,” in astronomical units (A U), and the numbers zero through 3 point 2, in increments of zero point 4, are indicated. The vertical axis is labeled “Density,” in grams per cubic centimeter, and the numbers 3 through 6, in increments of zero point 5, are indicated. The graph has 7 data points. Three of the points are grouped in the upper left corner of the graph, below 1 point 2 A U and above 5 grams per cubic centimeter. The remaining points are above 1 point 4 A U and below 4 grams per cubic centimeter, with 3 of the points grouped in the lower right corner above 2 point 2 A U and below 3 point 7 5 grams per cubic centimeter. The line of best fit is also graphed. The line of best fit passes through the following coordinates on the grid. All data are approximate: zero A U, 5 point 7 5 grams per cubic centimeter. Zero point 8 A U; 5 grams per cubic centimeter. 1 point 6 A U; 4 point 2 5 grams per cubic centimeter. 2 point 4 A U; 3 point 5 grams per cubic centimeter. 2 point 9 A U; 3 grams per cubic centimeter.

The scatterplot above shows the densities of 7 planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown. An astronomer has discovered a new planetoid about 1.2 AU from the Sun. According to the line of best fit, which of the following best approximates the density of the planetoid, in grams per cubic centimeter?

  1. 3.6

  2. 4.1

  3. 4.6

  4. 5.5

Show Answer Correct Answer: C

Choice C is correct. According to the line of best fit, a planetoid with a distance from the Sun of 1.2 AU has a predicted density between 4 point 5 grams per cubic centimeter and 4 point 7 5 grams per cubic centimeter. The only choice in this range is 4.6.

Choices A, B, and D are incorrect and may result from misreading the information in the scatterplot.

Question 366 366 of 368 selected Ratios, Rates, Proportional Relationships, And Units E

How many meters are equivalent to 2,300 centimeters? (100 centimeters=1 meter)

  1. 0.043

  2. 23

  3. 2,400

  4. 230,000

Show Answer Correct Answer: B

Choice B is correct. It's given that 100 centimeters is equal to 1 meter. Therefore, 2,300 centimeters is equivalent to (2,300 centimeters)(1 meter100 centimeters), or 23 meters.

Choice A is incorrect. 0.043 meters is equivalent to 4.3 , not 2,300 , centimeters.

Choice C is incorrect. 2,400 meters is equivalent to 240,000 , not 2,300 , centimeters.

Choice D is incorrect. 230,000 meters is equivalent to 23,000,000 , not 2,300 , centimeters.

Question 367 367 of 368 selected Percentages E

There are 320 marbles in a container. Of these marbles, 10% are red. How many marbles in the container are red?

  1. 32

  2. 288

  3. 320

  4. 352

Show Answer Correct Answer: A

Choice A is correct. It's given that 10% of the 320 marbles in a container are red. Therefore, the number of red marbles can be calculated by multiplying the number of marbles in the container by 10100, which gives 320(10100), or 32 .

Choice B is incorrect. This is the number of marbles in the container that aren't red.

Choice C is incorrect. This is the total number of marbles in the container.

Choice D is incorrect and may result from conceptual or calculation errors.

Question 368 368 of 368 selected Probability And Conditional Probability M

The table summarizes the distribution of color and shape for 100 tiles of equal area.

  Red Blue Yellow Total
Square 10 20 25 55
Pentagon 20 10 15 45
Total 30 30 40 100

If one of these tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction, not as a percent.)

Show Answer Correct Answer: .3, 3/10

The correct answer is 310. It’s given that there are a total of 100 tiles of equal area, which is the total number of possible outcomes. According to the table, there are a total of 30 red tiles. The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes. By definition, the probability of selecting a red tile is given by 30100, or 310. Note that 3/10 and .3 are examples of ways to enter a correct answer.